But her thread title says invest! She says she wants to use the money effectively - how is paying off her mortgage effective as an investment? She's vulnerable, as she is on a lowish income with no savings and the only way to get to any cash in the future would be to do equity release or sell her home and downsize, which costs money for no gain whatsoever.
She says she has hardly any savings and not much in the way of earnings. With a relatively small mortgage on her home she could probably pay it all out of the rental income on an investment property, and still have some left over, which she could either keep for herself or use to pay down her mortgage a bit quicker. If she earns a low wage now then the extra income from rent is unlikely to push her into the next tax bracket. Although if she could swap her current mortgage on her house to one on the rental place instead, she still owes the same amount of money, and her exposure to risk/rate rises etc. is no different, she will still own one house outright, but her mortgage payments on her investment property can be offset against any tax due. You only pay tax on the profit you make. So I agree that paying down her own mortgage would be sensible, but I would recommend she transfers that borrowing to an investment property instead, for tax reasons, rather than just having no mortgage and no extra income.
Just using the money to pay off her own mortgage is comforting but it's hardly effective.
Plus if she ever did need to get to any of that cash she could sell the investment property (hopefully at a profit if she keeps it long enough) without having to either borrow again to take equity out of her home, or having to sell her home.
If she was ever made redundant or become unable to work due to illness then she would be forced to start eating into the equity in her home to fund herself, so she'd just be spending that 100k. If she has a second home that is providing a small income it gives her all sorts of other options.
If she is in her 50s with a low wage then she will find it hard to obtain another mortgage in a few years time, and may end up having to do an equity release thing if she is short of cash. If the money is ring fenced in a separate property it can not only make her money month on month and potentially make a good deal of money in capital appreciation (eventually), but ultimately, if she is able to continue working and paying off the mortgage she has (whichever property it is on) she can own two properties outright instead of one. How can that be a bad thing?
If her current home is bigger and more appealing as a rental property and would command much more rent than the investment property then when she has the option of moving into the second property for a while (after retirement if it is a good distance away from where she currently lives and works) and making an even better income by letting her bigger, current home in a more expensive area (presumably) instead. It's a no brainer if you ask me. 
BTL is only very risky if you borrow (against your home) too highly to fund it, and you are the victim of sudden interest rate rises that wipe out wipe out any profit on the rent, and the value of the property plummets simultaneously.
If you think you can borrow beyond your means without doing your due diligence, to 'get rich quick' then you will get stung, for sure. But if the OP can afford to sink that 100k into a long term project then even if she sold the house in 10 years time for the same price she paid for it (pretty unlikely actually, over a 10 year period) then having factored in all the rental income over ten years it would still have been a pretty sound investment, and she gets her 100k back at the end of it!
In the case of the OP, there are plenty of places in the country where it is still possible to buy a very rentable 3 bed house for under 100k. Yes there will be a little leg work involved, and a little risk, but as investments go it's pretty hard to beat compared to most other things she could be doing with the money.