That is a pity that the physios at the NHS won't provide some help. In fact that is quite poor practice. Progressive resistance training and getting fit does improve outcomes after surgery so not providing this support is a false economy.
In light of that and that you don't want to go to a gym, (which I fully understand) have a look at this page:
Knee Replacement - Patient Education Guide
It has some of the exercises you listed. With the:
- Terminal Knee Extension: Short Arc Quads and
- Terminal Knee Extension: Short Arc Quads
both these exercises can be made more effective if you add a weight to go around your ankle. Weights can be improvised by putting unopened food cans of plastic drinking bottles filled with sand or pebbles in a pair of socks and tying you’re the socks together and hanging over your ankle like a saddle with even weights on either side. A good starting point would be so that you can complete 15 repetitions of the exercise in succession and by the time you get to the 15th the muscle is getting tired and the weight feels like it is getting heavier. If the exercise is sore to do from the start or causes pain later then just take it easy and slowly work up to greater resistance. Give your body time to get used to the exercise. If you get creaking and cracking on the movement that in itself is not problematic as long as it isn't painful or brings on pain later. Sometimes the exercises will never be comfortable during the exercise but it shouldn’t be overly painful and the pain should settle quickly. As your legs get used to the exercise you can increase the weight so that you can lift only 8-12 repetitions. This is ideal for strengthening.
Another exercise you could do is standing up from a chair and sitting down again. Do the exercise slowly (no sudden movement so you can't use inertia) and practice really sticking your bottom back as you sit down. You can start on quite a high chair and increase the effort over time by using a lower chair or couch.
With strengthening exercises just introduce one at a time, so your joints and muscles can get used to them. Ideally you want to work up at that level where you are working quite hard. You should only exercise every second day. This gives the muscles time to recuperate after the exercise and actually gives you a better result than exercising every day. But you do have to build up to exercising quite hard.
Another thing to consider is building up your general endurance. This can get you really fit without overstressing the arthritic joint and is also a good medium for improving the endurance of the knee muscles. Do you like the water and can you swim? This is where a warm pool would be good particularly if it is disability access. In the pool you can do resisted walking and (even jogging if it feels ok). Even better would be to join a hydrotherapy group is such a things exists. If you do like the water this can be more fun way of exercising.
By the way if you are aiming to really get fit just make sure you have a "warrant of fitness" from your Dr to exercise. This is important if you are over 65 and particularly if you have any heart problems, high cholesterol, depression, hypertension, obesity, diabetes etc.
Have you approached your Arthritis Society?
Arthritis Care : Welcome to Arthritis Care
Have a look under the "in your area" section. You may find they can offer you something