My father is a Justice of the Peace, he presides over debt matters in addition to traffic and parking tickets and other minor issues in Provincial Court in Canada - and our laws are very similar (as our entire court system is based upon British Common Law)
Here is my advice (from the conversations I have had with him).
Document EVERYTHING. Starting at finding and fixing the leak, right up to all of your interactions with this goon squad of a collections agency.
Make an offer to pay - I am sure that their "calculator" is a load of bollocks - did they even have an extended discussion with you over what your monthly ins and outs are? Make sure your offer is reasonable for YOU. Do not discount the importance of continuing to put money into emergency savings, account for incidentals, and do not allow it to negatively affect your DC(s). Take an evening with a cup or two of tea and some choccies and go through your budget line by line. Allow an extra 5-10% on each variable amount for unforeseen increases.
Again, document, document, document. Dates and times of all contact. The name of the person you spoke to (or their refusal to provide it, if that is the case). All of this will support you, and DO allow it to go to court if you cannot reach a settlement. However, don't play your hand to the agency representative. Just continue to document and tell them that you are sorry that you are unable to pay the £333 they are demanding, and guess that court proceedings are inevitable.
You'd be amazed at how many debts are reduced massively or rendered null and void because a collection agency refused a reasonable offer of repayment (and if you can honestly only afford 10 quid a week, and can support it with your budget breakdown, that is a reasonable offer - this isn't a mortgage we are talking about).
Deep breath, you are OK. Collection agencies rely on intimidation to make their money, and there is a strong likelihood that the agent is working for a commission.