I've recently started to pray but I'm having difficulties with fajr and the timing. I'm from the uk and at my local mosque fajr start time is 3.05am but dawn is at 4.07am will my prayer be accepted or have I been praying too early
There are multiple definitions of “dawn”. You have probably looked at the beginning of the “civil” morning twilight, which is after 4 AM. The correct twilight to use for the UK appears to be the nautical twilight. See here for more details on the multiple twilights as they apply to London, you can enter your particular city in the search box if you live in another part of the UK:
https://www.timeanddate.com/sun/uk/london
And here is a discussion of fajr and isha times in Britain:
Generally the mosques know what they are doing. You could try visiting the websites of multiple mosques in your area, their sites usually show the prayer times. Here is a random London mosque site that lists the fajr prayer time as 3:04 AM (see the top right):
http://www.eastlondonmosque.org.uk/
I'm from the uk and rely on a timetable for salah, but I was wondering is it better to determine when fajr starts by looking at the sky? for example fajr starts at 5.38am here but it's still completely dark, and I'm worried I'm praying fajr too early. I've read that the Nautical Twilight should be considered as the beginning of the subh prayer time.
The topography of your location determines how light or dark it will be regardless of the actual fajr time, therefore it is better to rely on the Nautical Twilight rather than relying on the color of the sky. Look up the website of a mosque in your city and they usually have a table of the prayer times. You can rely on that.