Claire,
I don't know the Army's Hat system so I assume 'Blackies' are mechanical trades. I also don't know which company has the Apache contract - either westlands, Serco or vector I assume?
Your employer may have some form of apprenticeship and may also have some form of technical training college, most of the MOD contractors do. Your first call is to enquire there - and see what they have to offer.
After that, if you can't move from the Ipswich area you should look at distance learning, as you first said.
"Licence by Post" is worth googling, but you may find it, or any others, expensive.
Some or your colleagues may have already tried this approcah and may still have some LBP notes that you could copy (or buy) Put a note on your intranet to see if anyone can help.
There are Licence websites like Part 66 .com that may also help - for a fee.
Even while you're doing this YOU MUST start recording your maintenance experience in detail and logging it by ATA Chapter - you will need to show that you have been working in an aircraft environment for at least three years to get a CAT A Licence. Your log is important.
If you need further please ask on here or send a PM. Ill post any answers on here to let others see them.
Rigga