TUPE allows for dismissal of an employee for Economic, Technical and Organisational (ETO) reasons and the stated reason for amending the hours of work on the contract which you have taken on are reasonable under this heading. The problem, as I'm sure you're aware, is that the resulting change is going to have a detrimental effect on the employee who you have taken on that she's likely to object to but your defence against a claim of unfair dismissal would be robust at an ET on the assumption that this is a demonstrable practice which, as you say, is carried out at all sites. That's not to say that it would be watertight since tribunals apply a narrow definition to the large areas covered under ETO but in the absence of all the facts concerning the transfer, that's as much as I can reasonably offer by way of opinion.
In your circumstances, I'd look for another contract within reasonable distance of the one the employee is working at and make an offer of employment which preserves her working hours but spread over two sites. It's possible that the employee would refuse this offer but, so long as the distance and time elements were reasonable, a claim for unfair dismissal would be less likely to be successful. Not every cleaning company has a mobility clause in terms and conditions (and they have their own limits in terms of enforcement in any case) but if I've made an effort to preserve the terms of the original employment then I'm a lot more confident about arguing my corner.
There are a number of factors to qualify the above and the two areas which I'd look at most closely are length of service and client perception. If the employee has been working for less than a year at the site then an unfair dismissal can't arise in any event (TUPE enforces employment rights; it doesn't generally add to them) and if the cleaner has generally been effective and is known to the client I'd think very carefully before making any changes at all.
