Evicting tenant with baby and wants to be evicted?

The easy answer is a section 21 assuming they are outside the fixed term and the tenants may have every intention of wanting to leave.

However, the key player in this will be the local council's attitude and how they perceive the tenant making themselves 'deliberately homeless' in their eyes.

Council often will not help a tenant find a new home unless they are forcibly evicted and often advise them of such and to hang on as long as possible. Therefore, it is important your tenant visits their council to see how helpful they will be. Obviously having a new baby will put them at the top of the priority list hopefully.

They shouldn't do this. But they do. They quote law and procedure in relation to landlords not carrying out their obligations but fail to carry out theirs as advised by the housing minister at the time.
https://landlords.org.uk/news-campaigns/news/housing-minister-writes-councils-over-evictions-advice-following-nla-pressure

Purely hypothetically,.........

I presume your tenant is just the male, and the female has simply moved into the same room with him as his guest?
If they had an argument and he evicted her from his room, then the Council would have to provide her and the child with emergency accommodation as she would be homeless and in priority need (due to having the child with her), and subsequently they would have a duty to rehouse her and the child (this could be in social housing or in private rented housing), so she would have a 2 bedroom property for herself and the child. If they then had a reconciliation and wanted to resume living together, surely he would just give Notice to end his tenancy with you, and then move in with her and his child?

The Homelessness Reduction Act came into force last April.
Councils have statutory duty to house those who become homeless. There is also a requirement that tenants inform their
local council as soon as they know they will become homeless.
With 3 people now in one room I would assume this is in breach of the permitted numbers under the terms of your HMO
license. In which case if you issued notice to quid due to this your tenants could not be considered to be intentionally homeless.

Due to inevitable house shortages, you are likely to be forced to evict. However, you may like to remind the relevant Authority of their responsibilities. See All Wessex article: http://www.allwessex.co.uk/local-authority-advising-tenants-stay-beyond-section-21-notice-period/ .

If your tenant wants to be evicted, should you not ask him to pay you for court fee, have you not already suffered some losses by other tenants leaving because of their baby?

So if he agrees to pay you court charges, then just go ahead and file a court application seeking possession under section 21 (which requires no reason) but needs to have been served minimum of at least 4 months after the tenancy had began, as well as meeting all other conditions such as having given your tenants all the required paperwork at the beginning of the tenancy i.e. copy of gas safety record, how to rent booklet, tenancy agreement , deposit protection prescribed instructions, etc, as an HMO you won't have to give a copy of an EPC certificate.
Since your tenant wants you to do this, why wait two months for the notice, set the date of notice as if two months have already lapsed, so the date is important so assuming 2 months have already lapsed, go ahead and file a court possession, why suffer two more months of loss of rent for other rooms.

It is good to have copertaing tenants to deal with difficult authorities. because they don't suffer losses we do.

Reply to the comment left by Mike at 24/09/2018 - 12:34
Are you suggesting dishonesty, and possible perjury?

Reply to the comment left by Michael Barnes at 25/09/2018 - 00:34No Micheal, my answer to you is very simple, i will keep it short just to avoid starting a lengthy debate on morality.
my answer is Yes and No, so giving you a choice, take your pick.

and remember if I ask you to jump off a cliff, will you?

Just one more thing Micheal, let us say you need to get down that cliff, you have two choices, one is jump directly down and land rough and possibly suffer some damage, or take a second route, go a long way through a path that leads to the bottom, I am giving you a choice you know the risk if you took a short cut. Taking longer path is safer, but cost you more both in time and money.
Another thing do we landlords not have law so much biased against us? we are always debating about various unfair housing acts, and how Landlords are being treated so unfairly.

BTW, Micheal, I have a tenant (couple) who occupy one room, since 2nd June this year they told me they were visiting Romania, for about 4 weeks, their rent due date is 12th of every month, i asked how will they pay me the next rent date that falls during their vacation, they said don't worry we will come back and pay you as they would only be about two weeks behind when they got back.
Micheal, they are still not back, and i am out of pocket having lost 4 months rent already, and the law which is so unfair, I cannot even get inside their room, unless I have a good reason to do so, now I must serve them a notice in their absence, and take the matter to court for a possession order, pay a court fees of £355.00, wait two more months, Micheal don't worry you do not need to jump off that cliff, I will., you just got me started, I have been a landlord since 1994. I could fill this section with so many cases of rouge tenants, and the law favours them unproportionally.