Welcome to the forum mate. Ignore the ■■■■■■■■■■■ Seems to be quite a bit of that on here with newcomers.
The jobcentre said no to me. If I had a genuine job offer then there is a good chance they would have paid for it. I got a refund of the costs of my 3 theory tests. If you are getting JSA you would be stupid not to ask them. Sometimes it may just come down to have an adviser who goes the extra mile or who has a bit of clout. Could make a big differenece to your bank account 
Good luck with your training. Sounds good to me what you are suggesting, not that I’m an expert on the matter 
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As one of the guys said might be better to give them a ring or send Peter a PM. I’m sure they can do something for you.