Start by checking your actual speed. This is the
official test site for connections via BT cables (irrespective of which ISP you're signed up with):
http://speedtest.btwholesale.com/
However this site usually produces fairly accurate results too:
http://www.speedtest.net/
[NB: To conduct a proper speed test you should ensure that your modem is connected directly to the socket where your phone line enters the house AND that your computer is connected to the modem with an Ethernet cable, NOT wirelessly. Once you've established a 'raw' speed you can then carry out a test using wi-fi to see if there's any great signal loss there]
As a rough guide, the minimum speed for streaming videos should be around 2 Mbps (but up to around 5 Mbps might be better for some sites).
Next, check what's actually available from your exchange by entering your phone number here and then clicking on the exchange name:
https://availability.samknows.com/broadband/exchange_search
In particular. look under 'BT Wholesale information' to see what's available to you. Ideally you'd hope to see 'FTTC' (fibre to the cabinet) shown as 'Enabled' but your posts suggests that it might not be. However it's likely that both 'ADSL' and 'ADSL Max' will be shown as 'Enabled'. If they are, go back to Sky and ask which service they're providing you with.
The basic copper-wired service that BT Wholesale sells to other companies is 'ADSL Max' (so hopefully you won't be told that you've only got the older 'ADSL'). However if you've already got 'ADSL Max' there's a variation on it, called 'ADSL 2+' that many ISPs aren't keen to tell you about (because they have to pay BT Wholesale more to use it). ADSL 2+ effectively DOUBLES the speed available through an ADSL Max connection so, if you've not already got it (and FTTC isn't available to you) you need to push hard to get it.
It's also worth remembering that some browsers seem to work far better with slow internet connections than others do. So try some different browsers to see if pages will load quicker for you in one particular one. (If you're using Windows 10 you've already got both Edge and Internet Explorer to try but also try Firefox and Chrome, together possibly with Opera, Avant and Vivaldi).
Remember too that some anti-virus programs can slow computers to a crawl. In particular, Microsoft's own offerings (Microsoft Security Essentials and Windows Defender) have seriously impacted upon the performance of several different machines of mine (particularly with the speed of loading web pages). Norton seems to create similar problems for a minority of people, as does Kaspersky and AVG. Try changing your anti-virus program to something else. (My own recommendation is Avast).