Excuse my ignorance but do civvies get an allowance for getting from home to work?
No. But under certain terms of duty one can get "travelling time" but it is rare. Typically, you don't get an overnight stay unless you miss the last train or bus because you have worked late - and even then it is not unknown for beancounters to say you could have hitched (seriously!).
Civilians above a certain grade are termed "mobile" and can be posted at 3 months notice anywhere in the UK. The only real difference to the Services is if they don't turn up they are deemed to have resigned instead of being declared AWOL. This is essentially what happened when, for example, AbbeyWood opened. Most lost a fortune, not least from spouses having to give up jobs and Bristol house prices rocketing as soon as MoD announced the move.
Also, one can reasonably be expected to travel up to 3 hours each way, each day, from a permanent duty station to a detached duty station, for up to 3 years, without being entitled to overnighters. At a permanent duty station, this reduces to, I think, 1.5 hours. That is, if you choose to live further away than a 1.5 hours each way commute, say from London to Bristol, you forfeit allowances. It is why so many civvies with very responsible jobs are on significant benefits. Not unlike many Servicemen I imagine.