There are many aspects to this and the sooner you can involve a professional who is familiar with working with TfL, the better.
One key question will be whether your husband made any admissions when speaking to them or not. (E.g. admitting to knowing all along he shouldn't have been doing this.)
Also, for how many years this has been going on, and were any false representations made during that period (applications/requests from the wrong address).
And whether there was any attempt to hide things from the investigation or whether the response was co-operative.
If this was triggered by a ticket inspection as you suggest might be the case, that may be helpful.
You need a solicitor to assess all the information then they may write to TfL setting out the options for resolution from your perspective. This may include a realistic assessment of ability to pay (having considered borrowing options etc.) over some time period - and then you have to hope that the solicitor can reach a negotiated settlement. If that settlement includes a criminal element, hope that it can be negotiated down to a minimal sample offence (the day of the ticket inspection) or set of offences rather than the worst case of full blown fraud over an extended period.
Time is of the essence, as the sooner a solicitor intervenes, the better the chances of stopping things getting worse. (I.e. persuade them it's not necessary to continue the investigation as there's a quick way to resolve it that would be acceptable to both sides. From their perspective, they have a big incentive to reach a quick resolution because if they no longer need to put any more staff hours into your case it frees them up to go after the next person and there is certainly no shortage of investigative work waiting for them! If you wait till they've already done 90% of the work, that argument becomes weaker.)