because I feel I can't really go up £8k now which is around what I wanted
Why ever not?
You are in a very strong position to negotiate. They want you , you have a job so don't need their offer. You are giving up continuity of service snd all the bother of changing, making new contacts etc.
Start by saying that you want the job but you just can't afford to take it at that rate. If they ask what you want, make sure you ask for more than you 'need' so you have some room to negotiate down.
They can offer more, and more benefits, better pension, starting bonus, pay review on six months.
You are playing into their hands if you think their making a low offer limits what you can ask for. As PP points out, this is their anchoring offer. You will never be in a stronger position to negotiate than now. It's in their interest to get you as cheaply as possible. You already know they want you.
Play the game, see what they offer. Enjoy.
Don't lie but do stick to your guns.