Brexit will probably hurt property values in the short term, but as long as you don't plan on selling in the short term, this isn't that big of a deal. House prices will eventually recover, and rental prices are less wobbly than house prices.

Be sure you know the costs of any common building maintenance fees, and if any big work is coming up that's not covered by those fees. Your landlady could have just gotten a letter that says "FYI, we need to replace the roof in the next year, and there's no money for that, so we'll be charging owners", and not wanted that extra cost.

The rule of thumb for repair costs is 1% of the property's cost per year. This is for single-family detached housing, though, and a flat is going to be less than that. You know your flat better than I do, though. For taxes, you should be able to get that info either from your landlady or your mortgage advisor. I'll note that your landlady was renting to you for £675, so that should be a reasonable guess as to mortgage+maintenance+tax costs.

However, it is not necessary for incoming rental income to completely pay mortgage and maintenance. Recognize that you're accumulating ownership in the property, and that has value as well. That being said, you won't have a renter 100% of the time, and it would be bad if you can't manage the rent on your new flat along with mortgage and such on this property.

Consider if you and your partner want to buy it together, or if only one of you should buy it. Relationships end, and once you have real estate involved, ending a relationship can get ugly. (Only thing worse are kids.) I don't know if you've been married 10 years, or just got together last month, but consider each of your individual interests as well as a couple, and make sure you have a plan in place in case you disagree about what should be done with the property, as well as how the money is split up if the flat is sold/rented.