So due to the vociferous opposition of some people to such heretical concepts as, the Gladiator might have trouble with an A6M, or that the Swordfish might be a little less capable than the D3A, I often get into the position of becoming the nemesis of the British.
This isn't necessarily my point of view, and to kind of balance things out I'm going to try to realistically assess how the RN might manage this situation. First having seen some of the disadvantages, what are the advantages of the British?
Radar
Encryption (probably breaking the code, their own code is likely unbroken)
ECM / ECCM - including things like tracking enemy ships and planes via RDF
General night fighting capability (in part due to putting radar on planes, even biplanes)
Excellent engines especially (but not only) the Rolls Royce
Very good interceptors
Discipline - almost as disciplined as the Japanese themselves.
Adaptability - the British are extremely cunning and can recognize new and seemingly ephemeral opportunities and use them to act decisively.
The British had several procurement or design related problems with some aspects of their kit in WW2. But they were also adapted to these situations with remarkable ingenuity.
I think initially, it's clear there will be setbacks. Ships, including carriers, are going to be lost. Island bases are going to be lost. But the British won't just sit on their haunches, they will adapt.
LF Spitfires
To deal with Japanese fighters like the A6M and Ki-43, there were basically three strategies. The first was to use fast roll and dive speed to flick away into a power dive to disengage, ala AVG / 23rd FG and 49th FG, 75th FS etc. P-40s. The second was to use careful group tactics Thach Weave to protect fighters and force the Japanese into an attrition situation, as was done with some success with the F4Fs. The third was to just overcome the agility of the IJ planes with sheer power and high combat speed, which is what the P-38 and then F6F, F4U, P-51 and pilots P-47 did.
I see an opportunity here with Spitfires. Initially, maybe it's not such a great match. But if you take a Spit V and clip the wings, now you have a phenomenal roll rate, faster dive and a much higher speed at lower altitude. You'll still want some 'regular' Spitfires for high cover but the LF types could prove to be very deadly. When Spit VIII shows up, you get this plus better range, plus increased high altitude performance which is going to become a problem for the A6Ms and Ki-43s.
Beaufighters and long range torpedo bombers
Right out the gate almost, you have Beaufighters. These had a pretty good record against A6Ms, for reasons I don't fully understand. I think high low altitude speed and of course, heavy firepower. I can see Beaufighters escorting aircraft like Wellingtons or Beauforts on long range, sea level torpedo, strafing and bombing strikes becoming very dangerous for the Japanese. Eventually you get the Beau's themselves carrying torpedoes.
Mossie?
There is also the Mosquito. They had some problems with moisture in India but what if you did something like the Russians did with Yaks and put a thin layer of bakelite over the fuselage. if you could fly Mosquitoes out of say, Darwin or maybe even Port Morseby, you could really pose a major problem for the Japanese both with high speed recon and strikes.
Coordinated naval battles in ideal conditions
As for surface combat, again I see trouble for the RN initially, (depending on the weather conditions) but they will adapt. Just as the Japanese torpedoes and night combat skills will probably be a nasty surprise for the British, the radar equipped night flying Swordfish and Wellingtons could be a very unpleasant surprise for the Japanese. So could radar equipped battleships and cruisers. Several times in the various Pacific battles, the navies were separated by weather. British ships could 'see through' the weather, as could British strike aircraft. They could deliver some punishing blows to the Japanese that way.
And if they broke the Japanese codes, and protected their own, which seems likely considering how sophisticated they were in this field, they could chose their moment to strike very carefully. They may even sow confusion in the ranks of the Japanese with some misdirection, as they did to the Germans on a couple of occasions. I see this path as the means to counter the Japanese naval threat to some extent.
Ground Forces - Churchill Tanks
The RN also has the potential of strong land forces if they bring enough troops and kit. As we know, the Japanese were no slouches in island defense but if you say, land Royal Marines and Paratroopers in Malaya, and (assuming you have the landing craft available) I think Churchill tanks could be pretty effective in a land war in some places. I don't think the Japanese have anything that can contend with these, and some of them have good 75mm guns.
Stoicism and Industrial Strength
The British are stoical. So are the Japanese, but the British are better positioned for attrition war.
Submarines?
The British might have an advantage here too I'm not sure I don't know enough about IJN and RN subs yet. But if the RN subs are as good as some have suggested, in theory they could get an early start at commerce raiding against the Japanese, which could cause them all kinds of serious headaches as almost all of their key supplies come by ship.
Air Sea Rescue and Recon
The British have a fairly large number (700+) of their excellent Sunderland flying boats. Heavily armed and capable of killing submarines, they are probably a challenge for A6Ms and Ki-43s the same way that US heavy bombers were. They also have this vast fleet of 'escorts' and destroyer escorts which can act as rescue ships for downed pilots and crew. This will ultimately work out the same way as it did for the USN, improved ratios of survival for the attrition war.
Impunity
There is no way Japan can attack Britain directly. They almost certainly can't invade Australia or New Zealand either.
Night strikes
British have heavy bombers that can fly from distant bases to hit Japanese ports, airfields. The Wellington has 2,500 mile range, and other heavy bombers which came later were close to that. That means bases like Saigon or Taipei might be in range of long range strikes from Ceylon or the Bengal region. And if they can capture some big enough airfields close enough to Japan, the home islands themselves. Japan struggled in night time air combat.
Overall
I think the Japanese have a chance to knock out the RN early. This is due to their marked technical advantage in the carrier war, and strengths they showed in real life in surface combat at Java sea, in the sinking of capital ships at Singapore, conquest of Malaya, fighting in Burma etc.
But due to the fact that the British can retreat to India, Australia, New Zealand etc., it will be hard for the Japanese to deliver a knockout blow. They could send ships to attack India, and they may well wreck the RN fleet there, but i don't see them successfully invading or conquering India. Not saying it's impossible but... really hard. Same with Australia. Unlikely IMO. So the British will have a chance to re-assess and come back.
The British do have some kit which could be adapted to victory. And the longer the war lasts the more of a disadvantage the Japanese have. The British are better positioned for attrition warfare.