If you have good relationship with your managers you may not feel like bargaining. £7k doesn't sound much assuming this is on annual salary. But those 1.5 hrs of commute you are saving can be much more beneficial. You are recovering about 8% of your waking life which could be spent in better way.
In the long run you know this new job is more beneficial for you. So start talking to your managers, not for bargaining but to explain your scenario. Tell them you do need to quit, but give them time to plan your departure so that there is no feeling of betrayal. If given some time, they can recruit someone capable enough to take it over from you. If the other company really wants you they will relax their joining date.
But before you talk, you should make up your mind on what you want. All the best.