I've got fret buzz on the following frets:

8th fret E string.
8th fret A string.
No buzz on the D string.
7th fret G string (very slight - Nearly inaudible over the sound of the note being played)
Slight buzz on all frets of the B string. Not really an issue, but it's still there.
No buzz on the e string.

I'm not playing very hard to make it buzz.
I have previously raised the height of the bridge by a few mm but it didn't make a noticeable difference. I was thinking that I may have some uneven frets but I'm not sure how to check for this.

Does anyone have any advice? If you need any further info I'd be happy to provide it. Thanks
see if the strings are hittin any other frets, like put e on the 8th fret and follow its along until you can see where the its touching.

Probably most likely higher the acton.

tl;dr - take to the guitar man of your town.
From what you have said it's really imposable to advise or say what all the problems are.
Sound like your frets need dressing [or possibly replaced even] and everything professionally checked over and set up.