each surgery has a "catchment area" rather like schools. If you fall outside of your g.p.'s catchment area they will ask you to register with a new gp. It is not sensible to hide your new address from your gp for several reasons
1) if you need a home visit they wont come
2) similarly, if you need district nursing or midwifery or health visiting services they wont come
3) lots of practices undergo "list clearing" especially in London, where there is a high turnover of patients This is when they write to you, and if you dont respond they strike you off their list assuming you've died or moved. If the letter goes to an adress you arent at then you wont be able to respond, and you could find yourself in the position of not being registered and thetrefore not being able to see someone quickly if you need to.
These things are especially important if you have a long term medical history
Look on the brightside, the new gp might be even better than the old one