As Pohutu says, you might find it cheaper to book on-line from UK sites. You may find that not all UK agents will let you do it, since some insist on a UK address, or at least they used to. This may have changed however now that e-tickets are the norm,
E-tickets, no problem. But
on routes where serious differential pricing exists and there is a potential problem over people in one country buying the ticket in the other, then the airlines look for proof of permanent residence for the country of ticket purchase at the time of check-in. For example, on a route with serious differential pricing, if you buy the ticket in the UK, this could mean having a valid UK passport held by you, or a passport from another country with the UK permanent residence visa stamped in it [or whatever system is used in UK to show permanent residence]. Of course, your frequent flyer address will be in the UK, won't it
In case of doubt, they could also ask for you to show them more proof of residence such as a valid drivers license from the UK.
And this is before the big guns get turned loose. Such as the 'Revenue Integrity' program from Sabre, or Flash or Zeus, or the Calidris Operational Data Store to analyse the various revenue leakages that occur. Travelport have 'Fare Verified' to make audits to check that tickets have been issued correctly with respect to fare class, rules, taxes, fees and commissions. Most ticketing errors come from six revenue integrity issues: fare errors, exchange rate calculation errors, incorrect commissions and taxes, incorrect refunds, incorrect segment and booking fees, and booking and ticketing violations. They know where to look, and the software systems are helping them.
The revenue leakage software audits fares issued and then makes a report that lists the locator code of each ticket and passenger name, the ticket number, the agent ID number, where ticketing errors have come from, the old fare, the new fare, and the difference that has to be applied. And does it quickly enough that the airline can go looking for the source of leakage (pre and post flight), and then move to plug it. This includes not honouring the ticket when you show up at the airport (and if they cancel the one leg of your ticket, the remaining ones get canceled automatically). Or they rebook you at the proper fare, prevailing at the time, which can be the very fullest economy fare (i.e. about 4 times more than you paid in the first place).
This is not an issue when there is uniform pricing, and many airlines with such pricing allow online ticket buying from anywhere . The low cost carriers are very good with this. I've brought online Easyjet tickets to fly all all over Europe and internal Aegean tickets in Greece, all done from Australia. And bought Emirates tickets from anywhere to anywhere using a laptop that is always in some other location.
So when the pricing is transparent and the airline allows you, online buying can be done from anywhere. It is only where there are significant fare differentials, and you know that you are bending the rules to buy the cheaper fare, that problems can occur for you.