The ITF only accept proposals to run their tournaments from national associations. How they then structure the financing of the event is up to them. In return for getting their name on Queens, Eastbourne etc, the LTA negotiated sponsorship from Aegon for all UK ITF events, British Tours and some junior events. Occasionally at BT or junior level an extra local sponsor will step in (last year there was a BT with extra prize money provided by a local sponsor) but all events have Aegon as the head sponsor as part of their deal. This is something I think the LTA should be proud of, getting sponsorship for sub tour level tennis events is no mean feat.
Have said before though, much more effort could go into advertising / marketing of these lower events in this country.
Challengers are run under ATP rules and regulations. There is no involvement of the ITF beyond a member body (national federation) signing off documents. Whether that body, the LTA, would or not give formal approval because of contractual obligations to a third party is a moot point. In my view, the LTA would be mad to spurn a private initiative to launch a Challenger simply because of some prior contractual obligation to Aegon.
At the moment, here in the UK the situation is way, way over-institutionalised. Everything, Wimbledon apart, is run by the LTA and the competition structure is accordingly weak. By contrast, go to a country with a basically bankrupt federation like Italy say, (Panatta ate all their money up!) and you get a ton of challengers (and ITF futures too).
It's trite perhaps, to suggest we still have a federation run by old school types when the game basically has gone professional. But that is exactly what it seems, rather akin to the RFU when Will Carling hastened the demise of the '57 Old Farts' who were strangling development of modern, professional rugby. A 'You can't do this' or 'You can't do that' attitude still seem to be the order of the day when it comes to tennis.
You can do whatever you want in life, tennis included, and an existing contractual obligation (if it exists) can present no bar if it's a reasonable, right and positive thing to do. More Challengers is one obvious area of progression for GB tennis. Plus a lot more thinking 'outside the box'.
the Aegon sponsorship is huge for a tennis association and I couldn't see any organisation risking losing that, putting off any future sponsors, and having to pay out substantial sums to extricate themselves from a reasonably long term contract for the sake of letting some smaller organisations sponsor a couple of below tour level professional events. Commercially it would be madness and not in the best interests of British tennis. Whether or not they should renegotiate the Aegon contract at its conclusion, or throw open the doors hoping to attract many smaller sponsors for challengers, futures, ITF, British Tour and national junior events is a different argument altogether.