This is not quite fully correct. In 1939, when Germany entered the war, the heer enjoyed quite high levels of motorisation. They entered the war with 6 Pz divs, fully motorised, 4 motorised rifle divisions, which more or less permanently had attached as independent units at least a bn of AFVs for support. There were about 5 "Leichte" divs, that in essence were light armoured formations. After the fall of Poland all of these units were converted to smallish Panzer Divs thus enabling the heer to enter the French campaign with 10 fully armoured divs.
In addition to that there were sizable formations of SS and the LW demonstation units, that ultimately became the HG heavy armoured Div (this happened later, but the assets were there from the outbreak of the war).
All of the 30 odd wave 1 Infantry Divs enjoyed high levels of motorisation, better than the equivalent British unit actually. They were assigned nearly 2000 vehicles actually. The standard line infantry ToE still called for just under 1000 vehicles per div in 1939.
The BEF quickly deployed to France in 1939, and initially consisted of 6 divs and 21000 vehicles. Many of these vehicles were not part of the divisional TOE, rather they were attached to the support echelons of each div. The supply head for the BEF remained at Cherbourg rather than move to the channel and thus massive dislocation of the BEFs support echelons occurred after Guderians dash to the sea had been achieved
The levels of motorisation for each division were good, but not as good as those top shelf heer formations in September 1939. Between September 1939 and May 1940 this fundamentally changed with the British army receiving massive amounts of motorised equipment. The BEF was equipped with no less than 87000 vehicles for the 10 divs assigned to the force. All of these vehicles were lost or destroyed. The 90 (or so) divs involved in offensive operations for the heer and its support echelons amounted to 660000 vehicles. In crude terms there were 8700 vehicles per div (including non- divisional support) for the BEF, to 7300 vehicles per div (including non-div support) for the heer. It is often touted that the german army was not motorised, and in terms of what happened 1942 and after, this is true, but in 1940-41, relative to their opponents, the heer was one of the most mechanised formations in the world. Its yet another one of those myths used to explain away why Germany lost…if only theyr were motorised in 1939….sorry but they were motorised to a very high level
Moreover, the depth of british preparations and planning compared to the bumbling efforts of the heer in subsequent campaigns is brought into sharp focus in what happened after Dunkirk. The BEF emerged from the campaign with virtually no equipment particularly for its vehicles. By the following February, these losses in material had been replaced and increased as the british army front line forces gradually increased.
The germans initially reduced the force structure of the heer after the surrender of france, then steeply increased as the decision to invade the USSR was made. German losses in soft skinned vehicles had been heavy during the French campaign, and production at home could not even keep pace with normal wastage, and German industry was slow to pick up the uptake needed to improve the supply of vehicles. They made a conscious decision at the time not to place their economy under strain by increasing military outputs, particularly for vehicles. The supply of spare parts and exchange engines remained far too low. Worse, despite repeated recommendations for rationalisation of the vehicle park, culminating in the Schnell plan, the numbers of different models in army service skyrocketed, made worse by the expedient of drafting into army service various lightweight (and unsuitable) ex-civilian vehicles and foreign manufactured vehicles (mostly french), that were fragile and completely unsuitable for what was about to happen
The vehicles per div (including non-div support echelons) had dropped to 4285 by the time of the Russian invasion, moreover OKOH at some point, without any rational reason to do so, had increased the radius of action for formations (the range at which military formations were deemed capable of operations from their supply heads) for Barbarossa, from 60 miles maximum in the west, to well over a 100miles for operations in the east. Such cavalier changes in operational requirements is utterly inexplicable , but as the inevitable happened and vast quantities of the flimsy soft skinned vehicles were lost and not replaced, the ability of the heer to project its force became less and less. This was made worse by the loss of horse drawn vehicles and draft animals as well which mirrored the crisis in the MT park. In 1939 there were between 5 and 7000 draft animals per div on average in the heer. By the end of 1942, this figure had dropped to about 2000 horses per div.
The effects of all this was that the highly mobile and effective force that existed in 1940 was largely immobilised by 1943. Hitler is often criticised for his stand fast orders, but in reality his order was more realistic than the heers stupid calls to withdraw. By 1943, a wholesale front wide withdrawal in the east was impossible, due to the shortage of MT and draft animals. Only by pooling of resources, closing ones eyes and praying that nothing would happen in quiet sectors was the heer able to shift decreasingly small amounts of the front intact