Will BT Internet or Sky let me cancel a new fibre-optic contract if the speeds are as low at 3mbps - 5mbps?

[Southpaw]

Well, first you have to find out if fibre to the cabinet is available in your area, so use BTs postcode checker;
http://www.superfast-openreach.co.uk/where-and-when/
Sky do not own any network infrastructure, the hire it from BT them rent it on to their customers for a profit, so it is the same apart from the router / modem.
BT have accurately calculated the upload and download speeds that you will receive when connected with an Ethernet cable, for WiFi you will be lucky to get half of that speed as it can be affected by distance from the router to your PC, and radio interference problems from nearby devices transmitting on or near the same frequency.
You will get the speed predicted if you connect with an Ethernet cable, it is science not guesswork, so in the unlikely event that there are any speed problems after installation you do have a good case to cancel, as ISP providers do not like bad publicity.
I have BT Infinity and get 39 Mbps down and 8 Mbps upload speeds using a cable, only 19 download speed though with WiFi.
The main advantage of it is that you can connect more devices to the router without losing speed, as there is more of it available.
The main disadvantage is that some websites as yet work at a much slower speed so you won`t see much improvement.
Due to the fast speed of optical fibre cables these days compared with ADSL copper wired connections it is not as necessary to throttle your internet speed as it was previously so that your neighbours could still get a decent service whilst you were abusing it.
I don`t think that you have much to worry about, you will get the speed advertised if you use an Ethernet cable between the router and your PC, regards, Bob.