According to their website, Debt Management Services Limited work for lenders where borrowers are in arrears or in other sorts of default. It is not that uncommon for lenders to outsource their recoveries activities to companies like this, as it is often more cost effective than to have an in-house team. You don't mention the amount of your debt, Meg, except to say that it is 'vast'. However, you do not say that you do not owe the money, so assuming you do, then the lender is almost certainly within its rights to appoint an agent to try and recover some or all of what you still owe. Unsurprisingly, the debt management industry is often painted as vultures preying on the weak, and in some cases this is exactly what it is. However, the idea behind the debt management company is to make some sort of recovery for the lender, for which they will be paid a commission.
If you have no net income and no assets but still owe the lender money, then you are likely to be technically insolvent, and should therefore consult the CAB or a licensed insolvency practitioner, who may advise you to petition for your own bankruptcy. This would have the 'advantage' of you getting a clean start in about a year, with all your previous debts written off, although if you own any assets now, most of these will be taken from you to be sold with the proceeds shared amongst your creditors.
The debt management company has no right to enter your partner's home (nor indeed yours if you had one of your own) and they are right to point out that they have no rights of distraint (acting like a bailiff). What they are looking for, I suspect, is a dialogue with you to ascertain whether there is any hope of any recovery for their client (your former mortgage lender), or whether their client should take steps themselves to make you bankrupt. Speak to them by telephone and tell them that you will seek professional advice, then go and see the CAB. You might well be better off bankrupt, if that's not a contradiction in terms.