To be honest, OP, this all sounds like a nightmare. Are you really sure you can't walk away?
First and foremost, you MUST ensure that you get the passports for these ponies- otherwise you will not be able to do anything with them. If they are in their 20s, they may not have microchips yet (they will need them by next year) but they legally need to be passported. If the owner claims they don't have passports, get them to sort it out before they sell the ponies. Purchasing a horse without a passport is an offense and you could (in theory) be slapped with a stiff fine.
There's a fairly reader friendly guide here, from the BHS: www.bhs.org.uk/advice-and-information/horse-ownership/horse-passports/faqs
I agree with the advice to get into contact with the British Driving Society- they may well know of someone interested in a pretty matched pair of ponies if they can still be driven! You'd also be surprised at how much horses and ponies can easily pull for their size- they can pull much more than they can carry. If they are very cute and friendly with children, there are also people who run "pony parties" who might possibly be interested as well. That said, in general it is very tricky to find homes for small or elderly or non-ridden ponies, let alone a pony that is all 3!
I also agree with the advice to get a vet out ASAP (either before or after purchase, pre-purcase vetting is very common when buying a horse). If these people are essentially willing to abandon a pair of ponies, then it's very likely they haven't been giving them proper vet care either.
Other people have been through some of the potential problems with homing these ponies, but I'll also bring up another issue. Equids are very social and most won't cope with being the only equine in a home. It's very likely that one of these ponies will outlive the other, and won't cope with being alone- so what would you do then? There are obviously options, but this could end up being a really long term commitment!
Finally, re: gun vs injection, I once saw a video of a zebra that was being euthanised via injection but wasn't given quite a high enough dose. It was really horrific to watch, and not something I could put any animal through, let alone a beloved pet. With a gun, it's always instant, and horses generally have no fear associated with a gun, as they might with a needle.