I'm planning on cycling from England to Northern Sweden, near Umea. My route would go through the Netherlands, Germany, Denmark. Are there long distance cycle paths I could take on the route? Is it easy to camp along the route?
There is no shortage of campgrounds in Europe, so it should be pretty easy for find a place each evening. But don't think you will be able wild camp along the bike routes (except maybe at a few designated areas). Much of the land along the bike routes is developed.
There are many marked (and mapped) long distance bike routes throughout the area. Actually there is one called the North Sea Cycle Route that might fit your needs to a "T".
There are also national bike route networks within countries like the Netherlands, Denmark, etc that you could link together to form you own adventure. Do a little googling for "long distance bike routes in XX" and you will find a wealth of options.
In all the area you will cover English is well known by a big percentage of the people, so you will not need to learn the local language, but you will be seen as polite if you know a few of the basics and ask whether people understand English, rather than assume they will.
When you search on travel planners for bicycle tours, you may find the fietsrouteplanner site. It has a Dutch name but these days the interface is trilangual, with Dutch, English and German. If you do run into some words you can not understand, you can find help on the site. It will find you cycle routes with sign posts, written books and/or GPS information and you can set the range of languages you are willing to accept that information in.
You may want to play with it a little, like setting more and fewer way points, avoid or allow ferries and sometimes even breaking the journey into bitesize parts.
On the other hand, if you want more detailed routes, more and more countries and smaller areas have bicycle route planners these days. In the UK, sustrance does well for recreative use, often off road and not very fast, I did enjoy using them but those who want to do 160 km/100 mile per day will likely not want them. In the Netherlands we have the nodule network, Fietsknooppunten, this is one planner that covers the whole of the country, in Dutch. Very good for recreational cycling within the Netherlands, but not as straight forward for long distances. Also as you will have to follow a new number every few minutes. But it makes for very short descriptions for bicycle routes. There are at least 10 different bicycle route planners in the Netherlands, covering different kinds of cycling, like commuting, day round tours, longer distances within the Netherlands.
Germany is slightly less well covered but still has plenty of coverage for cycling routes. And more in the norhtern parts you need than in the south.
I am not as familiar with what is available in Scandinavia, but by reputation you should be able to find both longish distance, commute and recreational day tours.
Camping will be easy to do all along the route, wild camping is not as easy.
In the Netherlands wild camping is not allowed (and there is really no space for it.) Other countries may have different rules and in remote areas you will find more options for wild camping or staying on farm yards and alike. On the other hand, if you want to stay in buildings, hotels and hostels aplenty in the UK, Netherlands, Germany and Denmark, further north it will be harder, specially if you get out of the local tourist season.
Some long distance routes lead you around towns, in which case you will may have to plan a bit farther ahead to find places to stay. Also (national) parks are often closed after sun down, so plan your times for that.
Food is (again) not a problem, supermarket and smaller shops aplenty, restaurants and fast food options, again harder to find when you get/stay off the beaten track. And when you use bicycle routes in some countries you may have to leave the route to find your shops and restaurants.