Thanks, will continue to ignore.

I have two debts with BT, one for over £200, one for less than £50, relating to broadband and telephone, which I do not acknowledge, for various reasons. These have been through 'SC Gray Solicitors' and 'Commercial Credit Services', both of which I think are the same. I offered them a settlement for about one third of the larger amount, by email, acknowledging no liability, they told me to call them, which I declined to do. Since then they occasionally call my mobile and send me letters, which doesn't bother me. I've checked my credit report and while there wasn't and isn't any reference to BT, there are three 'Outstanding Debt' searches by 'Pastdue Credit Solutions Ltd' made over the last four months, recorded in 'Table 1: Credit Searches'. Incidentally Pastdue just offered to settle for 60% of the larger amount having previously I think offered to settle for 75%. I think they might have given up on the smaller debt.I'm inclined to ignore it too, on the basis that they are liable to go down further and/or eventually forget about it. The question is do they have any right to record these 'Outstanding Debt' searches on my record? Can I get them removed?