Salt water/saline is a great thing to flush the wound with, but something with antibacterial/disinfectant properties would be slightly better. Many people use (on the advice of their vet) saline and F10 solution mixed together, iodine solution, or diluted hibiscrub. The thing is that something stronger to flush the abscess with may get the abscess cavity clean, but unless the capsule is removed it will re-occur.
The vet sounds quite good, but he doesn't sound like an expert. He's doing some things right - appropriate things to flush the wound with, and I assume he mentioned manuka honey? The thing is that rabbit abscesses are notoriously hard to deal with and need very aggressive treatment - abscesses in other animals may respond well to lancing and flushing, but rabbits don't. They need surgically removing in order to have any chance at fixing the problem. Rabbits need appropriate and often multiple antibiotics, as well as painkillers. Surgery is a necessity really, unless it's complicated for any reason - i.e. rabbit with existing heart conditions/intolerance to anaesthetic, or if the abscess is in a place where it's too hard to remove (i.e. wrapped around a bone/tooth or something).
Your bunny absolutely should be on pain relief - bunnies hide their pain very well. Please ask him to prescribe you some metacam. I'm frankly shocked that he hasn't put her on any
Please don't worry too much - with you cleaning it 2-3 times daily it shouldn't progress to any stage where you'd need to have her put to sleep. If you have her on painkillers it probably won't be affecting her quality of life too much. It's just that with this current treatment it's unlikely to go away, and if it does it will come back. It's very difficult because if it keeps coming back every few months you'll be spending a lot of the time treating her but not getting anywhere, and that's a horrible situation to be in. I've learned myself how heartbreaking it is to go through a load of treatment, only to know that it will re-occur. When I was with my old vet I felt she was doing the best she could, but I knew deep down that the treatment she was having wasn't going to fix her forever. I switched to a more experienced exotic vets who performed surgery and whilst the current treatment is quite hard work, it's soo much easier because I know that this treatment has a really good chance of fixing the problem forever.
I would definitely say your best course of action is to get painkillers asap, and speak to your vet about surgery and more aggressive antibiotics. If your vet isn't willing to attempt surgery I would look for another vet, and if he isn't willing to give you painkillers I would absolutely look for another vet asap. Not prescribing painkillers is terrible.
EDIT: If you want to change vets I would definitely recommend asking here in rabbit chat for a 'rabbit savvy vet in South Essex', and/or checking your local area for exotics specialists vets. Rabbits are classed as exotics, so non exotic specialists vets will not have the same knowledge that an exotics specialist will have. Rabbits are very different to cats and dogs, and what is appropriate for them may be wildly inappropriate for buns. From a quick google search, this place appears quite good:
http://www.southbeechvet.co.uk/exotic_pets.html