You could always find a good secondhand X2 teleconverter to take the 55-250 to 110mm – 500 but at the expense of aperture. Would only really work in good light.
And it won’t auto focus on that body at f8 or f11.
If you can afford it then the 2 cheapest realistic wildlife options are the 400mm f5.6 or the original 100-400 f5.6. The prime lens is optically better I think, but it doesn’t have image stabilisation whereas the 100-400 does. This means that the prime really needs a tripod or beanbag for anything less than 400ths unless you are very steady handed.
Both will be around £500-£600 maybe, but they will be massively better than the other options mentioned. Don’t put your own ability down, the glass is a huge part of getting a good wildlife picture. Just don’t start looking at the 500mm and 600mm, they really do sting the wallet.