I think you have two options.
You can go to Kwik Fit for a second opinion, and if there ‘professional’ opinion agrees with the servicing garage they will either contact Motability on your behalf, or advise you to contact them (depending on how busy they are) for permission to replace the tyres even though the tread depth is still legal.
You can notify Motability yourself as a first move to report that you have received this advisory (on 0300 456 4566) and ask for advice. They are very friendly and helpful. This would record the fact that you hadn’t ignored the advisory. They will probably suggest that you take your vehicle to Kwik Fit for a decision on whether the tyres need replacing immediately, or are considered safe to run on.