Have you looked into DAS costs for schools near you?
Absolute minimum you'll be looking at is £5-600 each, some schools charge £1k for new riders...
To get a decent 125 you're looking at £1500 realistically. Plus CBT puts that at £1800 on the road (ignoring helmet/kit cost as that will be the same). Do a few months on 125's and you'll then be able to do a 3 day DAS which is more likely to be £5-600 rather than £8-900 with zero experience.
Go straight to a DAS and it will be £8-900 for the course, then for a semi decent first bike I'd budget £1500, but you can pay a lot less.
The costs are similar, it all depends on the DAS course cost. I did mine with a trainer in Gillingham who was not only one of the best in the area, but one of the cheapest. a 3 days course with with both tests on the 3rd day was just over £500, not including CBT. I had 7000 miles and 6 months of 125 commuting experience at that point.