It's tax deductable extremely few places (US and Norway are the only generous ones I'm aware of; I'm sure there are more, but it's not all that common) and decidedly not in the UK. And you're right the money I give to AirBnB is gone forever, so I do need to take that into account.

However there are other issues to take into account: 1) it's not a given the added value of a room will be as high as the cost of adding it, and it can severely prolong the time before you're in the black. E.g. my house is one of the largest on my street already, and that typically results in a lower return for adding additional space, 2) you need to also consider whether the cost to cover the needs you otherwise would meet by adding a room is met by more, the same or less than the amount adding the room adds to your mortgage payments. If it is less, then it takes fairly little less before you're able to increase your capital faster by putting the difference in an index fund at the point in time when most of your mortgage payments still go towards interest.

By all means, it can pay off to build, and odds are I in fact will add a room to my house over the coming year whether or not it will be profitable. I'm not saying you shouldn't. Just that it's worth doing the numbers and figuring out what actually works best for you (and, yes, that does include factoring in equity) and sometimes the right choice for you might not be what is financially most prudent anyway. But it's worth going into it having run the numbers.