I have been playing an ESP LTD for the last two years and although I loved the sound and feel of the guitar, it was a a gift. The explorer shape really annoyed me so I sold it and bought monitoring speakers for production.

I'm now looking to buy a new electric but to move up to 7 strings and explore that realm of guitar playing.

I have a budget of up to £350 so I know there is not a lot of choice and I'm not sure what to set my mind on.
Any suggestions of stuff to look at would be welcome.

I play a lot in bands, church and at home, so I'd like to have a string lock on it too, but not exactly a Floyd Rose as I don't need the tremolo or vibrato, I wouldn't use it, I just want my strings to stay in tune longer. I can add one after I buy a guitar I'm sure, but i have no idea how to go about that so if it's already built on I'm a winner.

The main music I play is djent, metalcore and clean jazz.
I use a Spider 3 100w amp.

The best budget 7 string on the used market

But to start being serious, do you gig/band practice with the Spider? Cause if it was down to me, I really wouldn't want to gig one, even if it works fine for home practice.

At this price range, you aren't really going to get locking tuners or anything, so don't bother. Just look at getting a hardtail (Hipshot style, or TOM + string thru body)
But from what i've looked at, I think it'd be good to be looking at these, used or new.

Jackson JS-22
Schecter Omen Extreme 7
RG 7321 or a similar variant
Personally, i'd up the budget a little and get a RGD 7421.

I think one consideration to make would be do you want to go for extended range or standard 25.5" scale? That would depend on the sort of tunings you'll be playing in to be honest though.