I’m Irish. Taking the piss (I translated for a US audience) is the national sport.
But this, IMO, is a totally inappropriate context for it. Taking the piss out of a stranger you’re chatting with in a pub = normal. Taking the piss out of someone who knows absolutely nothing about you except that you want to move into her house, and who understandably wants some basic info = not normal.
Found the same and similar wording here and here. Sounds like a scam.
Shame, as she sounds quite funny.
The second part of her email seemed to include a lot of useful information (likes pets, easygoing, doesn’t smoke or drink, likes to date but not party, etc). I wouldn’t send this email myself, but I could certainly see someone sending it as a fun “here’s my personality” tone introduction.
ETA: Oh, jjimm, that’s disappointing. She seems like she’d be fun to hang out with.
There are two other red flags in the links I found:
“I reside in London,UK and would be relocating to the US soon”
“if am not around my roommate Jim would be.”
This is a typical habit of South Asian English speakers, not ones from the UK.
Yeah, so I’m gonna go with all the people saying “You Americans just don’t get British humour” were full of it. The ad response just screams fake.
She goes on and on about how correct she is, but her ad is full of typos and bad punctuation. Huh?
I think she’s a guy.
I wouldn’t immediately flag it up as fake just because of the jokes, which is what the OP seemed to be asking (apologies if I misread). The bit about “I and my Royal Doulton tableware will not”, as well as the fictional boyfriend shouting “Chuff me, how does she do it”, were both quite funny and wouldn’t send up any “wow, what a weirdo” signals to me, and I thought it was that the OP was asking about.
Scammer.
Google the first two lines of the ad response and you will see.
It wasn’t the “jokes.” It was written as though someone with no prior concept of written English language or punctuation ran some text through Babelfish. But it’s nice to know you kids would fall for this because it seems perfectly normal to you.
Yes, I probably would engage with this until the inevitable request to send money via Western Union or other obvious money scam came up.
Agree with both parts. If it was real, I’d say only a moderately slim chance she’d be a good housemate match, but pretty good chance the interview would be entertaining enough to be worthwhile anyway (assuming my levels of free time; I’m not chasing a two-year old right now).
News story:
http://www2.wnct.com/news/2010/dec/02/5/close-call-scammers-leaves-lessons-not-loss-ar-585906/
Jesus, why does local TV news reporting have to be so cheesy? I barely made it through that video without throwing my monitor across the room and I was actually interested in the subject. How does anyone watch this crap on a regular basis?
Do Brits use “roommate”? It’s very US to my NZ ears – I would always say “flatmate” but I’m not sure what’s common in the UK.
It’s not an either /or. 
Yes, the ad seems more than a bit odd… *and *many Americans seem to struggle with British humour. (And I daresay Commonwealth humour in general… not all, perhaps not even most… but more than a few IME).
I’ve heard both from Brits, but not sure whether they were speaking “English for foreigners” at the time.
i recently had a room for rent. i received many responses like the one you posted. they are all scams of some sort, though i only led one to tell me to send them enough money for a plane ticket to get here because " their money is in an account in a local bank and not accessible to them while not in the country"
I’m Scottish, and would only use roommate for someone I literally shared a bedroom with (e.g. in the dorms at Uni, or in a very very skint flatsharing arrangement!)
Most of the time, flatmate is the correct term.
And I don’t know anyone who’d say “chuff me”. Ever.
I’m British, and am amazed any fellow Brits think she sounds “fun”. She sounds to me like the epitome of the “I’m mad, me!” type who tries to make everything into a joke, quotes annoying catchphrases etc to hide their own complete lack of wit.
Avoid.
Yeah I love this show, doesn’t Hyacinth have periwinkles on them too? Would the OP have a sister with a big house that has room for a pony?