Basically, i'm trying to grow a watermelon plant

You have gotten a good start. Those look like healthy watermelon
seedlings (perhaps a little low on light, based on the tall stems),
and you can transplant them or thin them (having them stay that
closely crowded together won't work very well).

However, I'm not sure you'll get any fruit between now and when it
gets too cold or too dark. You can always try, and if nothing else
you'll get an interesting looking plant. But next year, start in the
spring with the watermelon.

As for what else to grow starting now, what springs to mind is cool
weather crops - chard, lettuce, spinach, carrots, beets. Maybe even
peas (here in Washington, DC they do better in the spring than the
fall, I'm told, because the vines take cold better than the pods, but
England might have a mild enough fall to be different). The main
challenge with many of those is getting them started now, while it is
still (relatively) hot. But if the seeds come up, you should be set.
If the seed packet says "80 days" and you start now, you should be
harvesting around the end of October or start of November. That
should be fine for the kinds of things I've listed here, which don't
need quite as much sun and heat as, say, a pepper.

I would generally aim to grow your vegetables outside (once they are
started anyway). While there are vegetables you can grow indoors, the
greater sun which is available in your garden will generally make it
easier (or in some cases, possible).