I was made aware by learning about British railways that unfortunately the slam-door trains are now gone.
Strictly speaking, not quite true. The Caledonian Sleeper (London Euston to Glasgow Central and Edinburgh Waverley on the Lowland Sleeper, Inverness, Fort William and Aberdeen on the Highland Sleeper), HSTs and MK3s in use both between London Liverpool Street and Norwich, as well as on the loco-hauled workings around Fife, Scotland still use slam-door MK3 coaches, not to mention the handful of MK2s on the Seated Sleeper portions of the Caledonian Sleeper. Oh and of course MK3 coaches on the Night Riviera sleeper (London Paddington to Penzance)!
Of course, I'm well aware you refer to the 'slam-doors' that were BR EMUs. It must be 10 years since they were withdrawn, 2010 I think for those which were modified for use on Brockenhurst to Lymington Pier services. Goodness that makes me feel old!
Hopefully when I get to London I will get some rides on a couple of 313's, 315's, and 465's, just to name a few.
Tons of 313s running between Moorgate (London) and Welwyn Garden City/Hertford North/Letchworth Garden City, so that won't be too difficult to do
315s every 10 minutes on weekdays between London Liverpool Street and Shenfield, as well as every 15 minutes on weekdays between London Liverpool Street and Enfield Town, with some also turning up to Chingford.
465s are also easy to do out of both London Victoria and London Charing Cross, as well as London Cannon Street. They go as far out as Dover Priory, although far easier to find on Metro services of course.
Might I also recommend trying some 317s (mostly operating out of London Liverpool Street) as they are usually quite entertaining. Of course, for maximum enjoyment get yourself into the motor coaches on all of the above, it won't be quite the same sitting in the trailer coaches!
I will try to get a ride on a Class 121 Bubble Car on the Chiltern Mainline, as I understood some of those are still in use.
Correct, Chiltern do still use a Class 121. This forum has the details of when they run (I believe it's just 121020 and 121034 that they use) in the Frequently Requested Diagrams thread, which should be a 'sticky' thread in the Allocations and Diagrams sector of this forum. Of course, these are subject to change and substitution by a Class 165 should the need arise, so check nearer the time. The 121s only run between Aylesbury and Princes Risborough, so no proper mainline running but I thoroughly enjoyed my run with 121034 a few years ago!
It's also worth pointing out that the UK has several cities which can be great fun for an enthusiast. Glasgow also has an extensive network with some very enjoyable motive power (314s, 318s and 320s), and the 314s have only a couple more years left before they're due to go. If London's not an option, I would highly recommend Glasgow as a very good alternative! Leeds is also highly enjoyable, the variety of motive power there is rather impressive, and of course you'll find plenty of the notorious 'Pacer' DMUs there! Manchester and it's extensive tram network (Metrolink, if you're not already aware), not to mention variety of motive power on local trains and large number of routes is also worth a look.
Not that I want to put you off London of course, it is after all that needs to be visited on a first visit if you want to sample the UK's railway in its busiest area, but just wanted to make sure you're aware we have several other places worth a visit!