@GrammarHopeful
You can commit to an independent school with an EHCP, as long as you are not planning to ask them to pay for the fees.
Your SENLA is not going to like it and they can be extremely pushy, borderline rude/intimidating to coarse you away from an independent choice, but as I said, if you are not planning to use their funding to pay for the fees, then nothing to stop you. I am also assuming that the schools know of the EHCP, have a word with school you want and explain that you believe this is the best choice for your child and are aware that the LA is not going to be thrilled. Then go for it, and after all is done and dusted, you can inform your SEN caseworker about it.
However, if you are planning to ask for the EHCP to pay for the fees, I would recommend you have good evidence to justify your choice, financial evidence that it will cost them less or ala par and a good SEN solicitor to fight in court.
I do know of a parent who had a full EHCP, sadly dad lost job and needed to move DC to the maintained sector. The SENLA asked why the move, they explained why and ironically it was going to be cheaper for the LA to fund the private fees, than the hours in his EHCP in the maintained sector. So it can be done as well. Mind you this was Sutton SEN and not Surrey (not holding my breath with Surrey SEN).
Best of luck in your decision.