Is DH giving the money to family reducing your potential spending to £2600? I think that would be tight.
If you were on 3400, with the money not going to family, I think you would be fine.
And 3000 is right in the middle of that! I think it probably is do-able, but not luxurious.
Costs to think of:
Rent
Gas&electricity
Phone/internet
Water
Council tax
Mobiles
Insurance
TV licience
Food
Transport - you say no car, but that is then likely to mean busses or taxis occasionally.
Clothes, birthdays, presents, meals out.
Saving an emergency fund.
I'm sure others can add to the list.
Are your family in the UK? Flights to visit them may also need to be factored in.
When we moved back to the UK, the first few months were incredibly expensive - we needed full uniform for both kids, basically had the wrong clothes for everything (average temperature had dropped 20C!), and there were all sorts of things we were presumed to have, and didn't (printer, colored pens, dressing up clothes, or clothes in a specific colour.
We also realised we needed e.g. pegs to hang the clothes out on the washing line, a bathroom bin..... it was endless for a bit. Have you currently got some savings?