In terms of the trucker shortage: the govt said today that the fuel driver shortage is small (150-300, tanker drivers make more than HGV drivers so probably true). BP said they were having no problems hiring but experiencing high levels of attrition (likely due to competitors offering pay increases)
BP met with the govt on Thursday, they said that supply levels were roughly at the level they had been since the start of the summer, low but manageable. Allegedly, they said they were only closing 10 or their 1,200 locations. They also said stock was low below normal levels.
Someone leaked this information to the media for the Thursday night news (it is very unlikely that it was anyone but the RHA). The person who did this left out several important details, in particular the fact that BP planned to close almost no locations. BP briefed the media later they were closing 20 (it was assumed initially that they were behind the leaks as the initial report was that the meeting was lobbying to lift visa rules, it seems not to have been the case). Other retailers briefed they had no issues with stock at all. Too late.
And the reason why people suspect the RHA is because they have been lobbying aggressively for most of this year to change visa rules. Visa rules were changed for them a few hours after this all kicked off (they also did poultry workers, this group have been working closely with RHA on lobbying)...this alone should suggest who is responsible.
RHA are, however, not backing down. This is not surprising as they are traditionally one of the most combative lobbying groups (the BMA is the other, SMMT has quietened down, NFU is combative but prefers to operate in the shadows when they are in govt). But, given that their lobbying has been successful, it is notable that they are continuing to push hard for further concessions (their line has modified ever so slightly though, they are talking about improving conditions...although they still sound quite angry that some HGV drivers are being offered £50k packages).
Unfortunately, lobbyists have worked out they have the media and the public in the palm of their hands. The outrage cycle in the UK has become rapid. After May folded to Nissan/SMMT (another lobbying group), lobbyists have realised there is a lot of money in briefing aggressively against the govt with a very pliant media (the RHA has been most aggressive by far, and has aligned itself with the big food lobbyists too). Brexit is inevitably part of this: 95% of journalists voted Remain, and there is a subset of the population who read a lot of news and talk about nothing but Brexit (if you are from the US, it is basically: what Trump did to Dems, what Obama did to Reps...it is non-stop).
EDIT: I made an error. The actual date of the govt meeting is not clear. Shapps may have said it was ten days ago, I am sure I read somewhere else it was on Thursday...I don't know. If it was ten days ago, that is obviously...unusual because the leak, most likely, wasn't accidental but premeditated. BP have completely washed their hands of it and claimed they weren't operating in the media on Friday morning...I don't quite believe that.