Honestly, I know you are anxious but please try and relax. As everyone has said, they won't be awarded anything in damages if they sue, because you haven't breached the contract and they have no losses. 0. The worst, worst, 0.0001% chance scenario is they pointlessly try and sue just because of vindictiveness, so your costs would be having to email or post the court the email you've sent them giving them ample notice that you no longer wish to enter into the contract which will result in the case immediately ending, so the financial impact would be what, 1p in electronic costs to use your laptop or phone to send an email or 20p for a stamp? And no, even in that highly, highly unlikely event of course it won't show up on a DBS because it's not anything criminal or involving the police, it would be a civil action like divorce or child custody proceedings, nothing to do with safeguarding, not the point of a DBS. Christ if everyone who ever had to go to court got a negative DBS check there'd be virtually no nurses, police officers, teachers or social workers left because stuff like this happens all. the. time. ... you have done nothing wrong and have nothing to worry about, please believe us.
They probably either haven't read the message yet or have but it isn't a priority to get back to you - there's nothing really for them to say to you at this point and if/when they do reply at most it will say thanks for letting us know and good luck for the future/what a shame etc so there's no point frantically refreshing your emails waiting for a reply, I know you will anyway but can you try and distract yourself a bit/snap out of the spiral, do you have techniques for this? Go for a walk, talk to a friend, watch something funny on TV? 