It is a voluntary code which the SRA are not part of. The SRA won’t get involved.
There is not an integrity issue with accepting and then reneging an employment contract.
The reality is all that could happen is that the law firm you renege on could seek damages for breach of contract. But are they really going to do this when there is no cost to them if you reneging and they can probably easily back fill your vacancy? The costs of seeking out a breach of contract claim would be more painful than just waving you goodbye and wishing you the best of luck with your future career, while they breath a sigh of relief that you turned them down (no offence meant by that, but a firm would much prefer you to turn them down now than not be truly committed to the firm).