The Eurostar provides nice connections between Paris/Brussels and London. Does it also provide a good alternative if you need to travel to a more northern destination. To put in other words: if I want to go to Manchester for example, should I also consider the Eurostar as an option?
The Eurostar arrives at London Kings Cross/St. Pancras.
From there you can catch the midland main line (to Sheffield) or the east coast main line (to Newcastle and Edinburgh).
If you wanted to go to Manchester you'd need to take the West coast main line from Euston (a 9 minute tube ride away).
As long as you don't mind changing trains, the Eurostar is a perfectly reasonable way of getting to northern England
The Eurostar goes to St. Pancras International station in London.
The Virgin Trains Pendolino service has a train to Manchester every 20 minutes, and takes about two hours. This leaves from Euston station, which is about ten minutes walk from St. Pancras. The public transport connections between the two stations are not very good, so I would generally walk; if you have a lot of luggage, or otherwise struggle to walk, then I would suggest a taxi; by the time you've walked to the platform for the underground and back up again in Euston, you might as well have walked from station to station.
I would recommend leaving St. Pancras via the Midland Road exit - it's signposted "Exit (Midland Road)" from inside the station, or also signposted "Taxi". There is a pedestrian crossing directly in front of the exit; cross there and then turn right. Walk alongside the Francis Crick Institute (currently a building site) and turn left when you get to the next road (Brill Place). You can walk straight along this road until you reach the side of Euston Station. There are two or three locations where the road is blocked for cars, but pedestrians and cyclists can walk straight along here. When you get to Euston (it's a large, ugly building that directly obstructs your way), cross at the zebra crossing and then turn left on Eversholt Street. After a minute or two, you will find a set of steps up to the right, signposted "London Euston" with the BR and London Underground logos. Go up the steps and Euston station is on the right.
Most mapping systems will suggest walking along Euston Road. This is a much more unpleasant walk (along the side of a main road) and considerably further - Google Maps, in particular, can't find the Midland Road entrance to St. Pancras and takes you out through Euston Road, a long walk inside St. Pancras station from the Eurostar platforms.
More generally, St. Pancras is very well connected to rail services for most of England and Scotland - you can use:
There are also Southeastern High-Speed services from St.Pancras (but also from Ebbsfleet and Ashford, which are on Eurostar) to various parts of Kent, like Dover and Folkestone.
The train systems that more difficult to get to because of connections in London are Greater Anglia to Norwich and Ipswich (leaves from Liverpool Street) and First Great Western to Bristol, Cardiff, South Wales and South West England (leaves from Paddington), both of which require a London Underground journey to get to the station.
While the combination of First Capital Connect and Southeastern High-Speed can get you to many places south of London, you might need to get to Victoria (Southern) or Waterloo (South West Trains), both of which require a London Underground journey, for some places.