There are several issues worth addressing.
The frame is too big, when I stand on the bike, off the seat, my toes only just touch the ground. I'm not thinking this is safe to ride around London.
When road bikes had top tubes parallel with the ground, if you could not stand over the top tube (i.e. out of saddle, straddle the top tube, put both feet on the ground), that was an indicator that the frame was too big. That's no longer true, since almost all frames have sloped top tubes.
On performance bikes, it is pretty common to sit on the saddle and be barely able to touch the ground. I can touch it with the tip of my toe, and I think my saddle height is a bit lower than average.
I am not sure exactly what your quote means. Please consider clarifying. What does standing on the bike, off the saddle mean? If your toes can't touch the ground, are you actually sitting on the bike's top tube? (If the latter is true, that bike is probably many sizes too big.)
If I change the wheel size, rims, to a smaller size will this lower the height of the bike?
This will lower the height of the bicycle. Unfortunately, bikes with rim brakes can't take smaller wheels - there is no means to lower the brakes. Bikes with disc brakes should be able to do this. However, you would also change the bike's handing away from the design parameters. Notably, I think you will decrease the bike's stability...
I measured the rims diameter 25 inches. If I got smaller wheels would this work?
I'm actually not sure what you measured as 25". There is an older wheel size called 26". The effective rim diameter, i.e. 2x the distance from the center of the hub to the bead seat (not to the top of the rim sidewall, this is where the tire beads sit) is 559mm, or about 22 inches. A 29er rim (same diameter as road bikes) has an effective diameter of 622mm or 24.5 inches. I am guessing you might be measuring from one end of the tire to another. If you have a disc brake bike, then I guess you could put in 26" wheels, which are an older spec, if you can find one which fits in your bike (e.g. does it have quick releases or thru axles; the latter will be a big problem) However ...
I've lowered the seat as far as it can, and the handle bars too.
If you need to lower the seat all the way, then yes, the bike is very likely to be too big. However, you can't actually fix this with a smaller wheel size. That changes how low you are to the ground. It does not change the length of the bike, or the distance between the bottom bracket and the saddle, which affects your leg extension when pedaling. Many casual cyclists set their saddles too low, and they won't be able to generate as much power.
So, why did you lower the saddle? Is it because you have trouble reaching the pedals at the bottom of the pedal stroke? That means the bike's too big and can't be fixed. If you just lowered the saddle because you can't touch the ground, that wasn't what you want to do.