Wrongly given lodger agreement instead of AST?

I am astounded that you would expect anyone to not have visitors / partners staying over in a scenario like this or that she ever agreed to such a restriction in the first place.
Would I be right in thinking that she does not have free run of your property?
I once had such a landlady and I moved out after three days.

Please tell me you're joking about the no visitor clause?

"Hi I mistakenly rented out a self-contained studio flat annexed to my house"
The above sums it up.You can't even take the moral high ground after asking her to lie as well.

I have an office attached to my house which I am considering turning into a self contained studio, but would not think of trying to say it is a lodger. It has a separate entrance like yours so it is clearly an AST and not renting a room or HMO - no shared amenities, you clearly know this by asking her to lie.
I take it all bills are part of the rent, electric, council tax etc which is maybe why you are trying to say it is a lodger.
I don't understand the no visitor rule (even as a lodger) in a self contained studio, it will not inconvenience you surely?
The smoking ok I understand, but most tenants say they don't don't smoke and clearly do.
I think you have got caught out and bought the circumstances on yourself. You need to speak to her and see if she will move out, if not you will have to provide an AST and try to plead ignorance, although this is no defence in law. If you catch her smoking you can then use that to try and serve notice, but I think the courts will firmly be on her side.
Take it as experience and a life lesson and be more honest in the future as the saying goes cheats never prosper.

You might have to eat humble pie here and just let her stay put until she wants to leave. Goodness knows how you stand legally on how to evict her.. Your 'no visitors' clause could be deemed 'unreasonable'. . If she has been with you just a short time I'd consider offering to refund her the rent she's paid if she just goes quietly .

Have you also been claiming that the income is covered by the £7,500 Rent a Room Allowance? Of course she is being "awkward" she has you by the proverbials!

“ Although I did tell her if anyone asked she should say that we share the kitchen and say she is a lodger.”

Does the person actually share the kitchen with you or is the property in question wholly self-contained and inaccessible from the remainder of your property? If the latter, you probably should have an AST, and even though you’ve called it a lodger agreement, I suspect it would be viewed as an AST in the eyes of the law. If not, and if you do genuinely share a kitchen, she probably is a lodger, which puts you in a better position In terms of obtaining possession.

Smoking is commonly prohibited in properties but the term with regard to no visitors does seem somewhat unreasonable - this is the tenant’s home after all. If the boyfriend is only staying over from time to time rather than living there that should be ok, but if he is living there that would likely be a breach of the terms of the agreement. However, enforcing possession these days (for an AST) will be difficult, and a negotiated settlement would probably be your best option if you cannot come to an agreement on whether and how you can coexist.

You can call the agreement whatever you like, but from your post it seems that in the eyes of the law it is an AST. Did you serve all the relevat paperwork with your agreement? "How to Rent" booklet, EPC, CP12, GDPR, did you take a deposit? is it protected?

It would appear that you are in deep doo doo & even if you could serve notice it would be 6M. As suggested above, best bet is to offer a financial inducement to leave ASAP, pray they accept & put it down to experience.

I am pretty sure a court would consider this an AST, irrespective of what any paper agreement states. You would have to give two months notice (assuming rent is paid monthly). The no visitor clause would be considered as an unfair term and have no relevance in a dispute. What you should be concerned about is that you are unlikely to have or have even served a current gas safe cert, tenant rent guide, EPC, deposite details (assuming you took a deposit). Basically I would withdraw you notice served and keep your head down!

Yep you're screwed, you put an unreasonable clause in and used a questionable setup with her as a lodger.
I'd advise you let her stay till she wants to leave, or offer her a goodwill payment to leave.
You would lose quite badly at court if you went down that miserable route.