A friend in London has asked me to help pay her BTA charge in order to fly to Ireland.
What is a BTA charge, and how do they affect your flight?

BTA is a base or basic travel allowance, and in almost all circumstances, they are an attempt at a scam. A UK or Euro Zone citizen (passport holder) doesn't even need a visa to travel to Ireland, much less a travel allowance. How well do you know this friend, and what are the circumstances surrounding the trip?

Agree, this does not sound valid, did they promise to "put it in the bank" and then give it to you as soon as they get back.

Also I will challenge that they are really a friend, if you had a real friend, you would not even be suspect and they would have known what was needed for their travel.

I suspect this is a dating scam and I bet they want you to send the money to them Western Union for various reasons, not mail them a check??

She contacted me through a pen-pal site, and has asked me to help her with a large amount of money once, saying she had a business worth hundreds of thousands of dollars, but couldn't access her bank account, and then furnished me with an address she claimed to live at to send the money to, which turned out o be a brasserie/restaurant.
Now she is asking me to not only pay for her flight to Ireland, but also the BTA charge at the airport.
I have contacted both the British Embassy and Heathrow Airport, who both say that BTA's are not existentn in the UK.
Is she trying to scam me here?

She has asked for the money to be sent by Western Union more than once, as she says she cannot give me the details of where she lives, as she is "living in a hotel," but claims to have no money, and no access to her bank account.
She also states that she will be refunded the BTA charge when she arrives in Ireland, but still needs me to help pay her fare and the BTA charge.
I've asked for details about her life, but she says she'll tell me everything when she gets here, and not before.

Who can I report this person to, as her demands for the money are becoming more intense day by day, and are getting on my nerves.

I think you have answered your own question here, but just to make it perfectly clear, YES THIS IS A SCAM. Block the person, ignore them, and run. These people are professionals, and they are successful because of their sympathetic sounding stories. Don't be sucked in my a professional con artist. Ignore any threats, and if you have given any bank account information or identifying details such as your social security number, please take steps to protect your identity.

ANYONE that asks for money transfer via Western Union, or similar, should be viewed with suspicious.
This is the favoured route of scammers as the money is untraceable.

This is a world famous scam, 1000's of people a week fall for this, This is one of the several versions.

Most likely she may not even be in that country, since with Western Union they can pick the money up anywhere.

But one one version, it is a dating site and in a couple of months they are deeply in love with you. I get about three emails a week, saying how much they loved my askme profile or my Facebook profile, I guess old priests are sexy to someone.
In the other, they have money either found, stolen or at some issue can't get to it, ( or gold hidden) and will share it with you, they play off your greed to get something for doing this.

It is a scam, check out ghana or African dating scam,
It all works the same way, 90 percent are actually located in Ghana since it is the nations best sourse of income, and often the crooks that operate these control the local police forces also

You can report the person to law enforcement, but it is likely that nothing will be done. This person probably not in the UK at all, and out of the reach of local police. Let them know you no longer wish to be involved with them, and leave it at that. Do not read any further emails. Do not answer any calls.

Just want to say thanks for all your help.
She offered to give me all her money when she came over, but as I'm a very spiritual man, with no materialistic greed, I refused to let her give me any money when she gotb here, which is when she started asking me for various amounts of money to be sent to her.
I have had trouble like this before (women offering me vast amounts of money) and it's always turned out bad in the end.
I'll just ignore her e-mails from now on, and have already opened up another e-mail account for myself, so she won't get to contact me if I can help it.
Thanks again, as she actually told me to come on this site in the first place, after I challenged her over the BTA charge after looking them up on the US Embassy site.