Presumably these 220B batteries are the sort that short circuit and burn down planes. You've just spent £1000 or so flying to the UK, then paying some exorbitant rent in London, but baulk at 40 quid. The battery needs to be an AGM type; they are the only truely sealed type.
Not sure why you need to. Motorbike batteries are available in the UK at Halfords. But I suspect the battery won't be allowed in your checked luggage, and it will need to be in the original box. Uni flight 673 came down because one person put flammible liquids in the overhead locker, and another person put a motorbike battery in an overhead locker. A resulting electric arc then caused an explosion.
Nope. Previously it was in person at post offices. Now it is in person at a Pay Point location. There are websites that promise online of digital IDPs. These are scams, and, if you actually get anything, issue counterfeit documents. Legit documents cost £5.50, fake documents from an American scammer are £42.
AA and RAC don't issue IDPs in the UK. Only the Post Office currently does. The Post Office though is losing the contract and its switching to Pay Point instead; basically participating corner shops. There is no online option. If not in the UK, you have to ask someone to commit fraud to get one.
You submit a budget? I thought the sponsor (me) merely states they will be responsible for all costs (submits Bank statement as evidence of income, savings).