You'll only fix it by getting a better broadband connection!
The pauses are due to 'buffering' where your computer has to wait for the next block of data to come through your phone cable. If your broadband speed isn't good enough your computer will frequently need to wait until it can catch up.
If you let the video play all of the way through, while you go to make a cup of tea, you should then be able to watch it without any breaks. (That's because the data will have been placed into temporary storage on your computer's hard drive, so you won't have to wait for it to struggle down your phone line).
Watching at times when the internet is being less heavily used will also improve your chances of getting the data to arrive quickly. (The busiest times of day are the few hours after the kids get home from school).
But you really need to look for an ISP which offers a good 'contention ratio'. In an ideal world you should have your own personal connection to the internet (called a 'leased line'). But the cheapest companies charge at least £400 per month for such a service (with prices closer to £1000 per month being more common). So you effectively have to share your connection with other users. The cheaper ISPs have 'contention ratios' of around 50 to 1 (so that you're sharing with up to 49 other people). Some even have ratios of 100 to 1, or worse. The better (but usually dearer) 'home user' services have a 30 to 1, or 20 to 1, ratio. (My own ISP has a 7 to 1 ratio but I pay 'business prices' for the privilege).
In the meantime, check what download speed you're actually getting, preferably at different times of the day:
http://speedtest.net/
(Don't click on the 'Run a free scan' advertising link. Go straight to 'Begin test').
Chris