HMRC are going to be unconcerned - The tax is being paid, and I don't suppose it comes from the individual or the employer.
The real issue comes down to what we should consider reasonable, fair and equitable in order to do the job. It is claimed that One of those guys needs a chaffeur driven car because of issues of Confidential documents. That may be possible, I suppose. Why do they all seem to need to travel first class on the train though?
And it is alleged that one of them was claiming the cost of commuting between London and the Lake District. Again, not sure quite why the taxpayer needs to fund that.
Although I will say - in one job I was in, I had to spend 3 days a week in my companies offices in Livingston every week unless I was abroad on business, commuting from my home in Hertfordshire - and the company picked up the cost of the commute be it air fare, train or fuel costs, and covered the cost of a small flat, so it does happen in the private sector too.