Firstly, they should not have been able to sell you ADSL if your location was too far from the exchange for them to offer a stable & reliable service - so that should not be an issue. Even if it were the issue, in all but the most extreme cases, the effect should just be lower speed rather than unreliable connection.
I'd ask Tiscali to confirm in writing whether your connectivity problem is because you are too far from the exchange to get reliable connection. If they confirm this, I reckon you would be able to cancel your contract on those grounds (if that's your preference).
Secondly, ask around other locals who use Tiscali & find out whether they have similar problems - the engineers will usually seek to pin the blame on your own premises to avoid doing too much work themselves, but if your neighbours also have the same problems then it's the ADSL kit at the phone exchange end of things that's at fault.
Next, while you are actually connected, do yo achieve good speeds? You can test that on various websites (eg.
www.kbps.co.uk - Speed Test Home). If this reveals that even when you are connected you get a low speed for the product you have purchased, then this indicates (a) you ARE very far from the exchange or (b) you DO have some telephone wiring issue somewhere between you & the exchange. If on the other hand this shows that you get consistantly good speed while you are connected, it would point towards the Tiscali (or TI) ADSL infrastructure being suspect. Save a set of speed tests at different times of day/day of week as this would support your case for further investigation if they show consistent high speed but you still keep getting disconnected.
The advice about extension phone sockets within the house is correct - very often, a badly installed extension socket or poor quality/loose cabling may interfere with the broadband signal. Have you tried to follow their advice, & if so, does it seem to help? i.e. with the extension unplugged, is your broadband connection reliable? If so, you should re-wire the extension (or maybe remove it entirely and use a wireless phone for the bedroom?).
In general, if you have an intermittant problem, the best thing to do is to eliminate all possible contributory factors and then add them back in gradually - so, ideally you would disconnect the extension cable from the master socket (you'd need to open up the socket and have appropriate tools to do that bit) & also remove all other telephone devices from the master (except the broadband bit). If the BB is stable like that, then add things back in order of priority: so, "main" telephone first, then any answering machine, then reconnect the extension cable (without the extension phone plugged in) and finally with the extension phone plugged in. Test each configuration, and if its all consistently stable until you add one more thing, then it's that thing that's the cause of the problems.
Your neighbours use of their own phones (OR broadband) should have no impact on your broadband stability. At worst, it may slow your surfing down if everyone is using their broadband at the same time, but it shouldn't disconnect you or prevent connection.
Finally - I'm assuming that you DON'T have a wireless router in the house that is, you only have broadband connected directly to one computer & you can't surf on a laptop anywhere else in the house? If you DO have wireless, that may often have a whole different set of problems (from thick walls to interferance by fairy lights, other peoples wireless BB, your cordles telephone, microwave oven etc etc). I'm sure though the guys who've ben to your house would have mentioned that if it were applicable?
Good luck!