Room/set top aerials seldom work well unless in a very strong signal area and mostly unobstructed view to transmitter. (Occasionally, upper floors may be OK while ground is impossible). Location is key to TV reception. Use
Wolfbane to give a very approximate estimate of the signal available (postcode or OS grid centres will seldom equate to anyone's home) and post the results (Transmitter, Field in dBuV and distance are the most relevant/needed). Alter the antenna height down to 1 metre from 10 to get a pessimistic figure/see if the numbers alter - it will be closer to the height of an outside aerial on the annexe?
An aerial cable could be run from house to annexe some way and the house aerial used to feed that (via a splitter, either powered/amplified or passively; depending on the signal lev. Overhead via a catenary wire, well supported and fixed to a suitable pole/bracket to be well above people's heads. An underground duct is an alternative. (How was the mains power and ethernet got to the annexe? If it was via a cable duct it may be possible to feed another through / lay anther duct the same route.
Protecting the cable from accidental damage is the greatest challenge. Plastic conduit can be helpful. WF100 and similar cable will attenuate TV frequencies by 16dB per 100 metres: 4dB for 25m. A 2-way splitter loses the same amount. A low gain (8-12dB) amplifier will make up for those losses, if there's not enough in hand from the aerial. Amplifier must be as close to the aerial as practical to work properly though.
Catchup TV services and live-streamed TV (iPlayer etc.,.) may suffice for some people and negate the need for a TV aerial altogether?