Where are fallen British soldiers burried.?

A lot depended on who won the battle!

Often fallen solders are buried in mass graves by the enemy. Some times the location is "unmarked".

The winning side often buries their dead with "dignity" and does not take time to honor the loosing sides dead with a "proper burial".

Keep in mind that even after fifty plus years they are still finding the remains of fallen solders from WWII. If the remains were not found, they were left to rot on the battle field.

The fallen soldiers would be buried in different cemeteries in different parts of the world, often dependent on their location when they were killed in action. Some soldiers would have been brought home and buried privately by their families, others might be in Government-funded cemeteries for fallen soldiers and some would remain where they passed away.

Most of them are flown home to be buried with their family's arrangements.

They are buried (note spelling) in cemeteries near to the battleground where they fell. These are maintained by the Commonwealth War Graves Commission.

Most are buried in cemetaries. Some, may be cremated, I suppose.

in a cemetary, just like everyone else

In cemeteries near the relevant battlefields, mostly maintained by the Commonwealth War Graves Commission. You can look for locations on their website. Nowadays they are transported back to the UK, notably to RAF Lyneham near Royal Wootton Bassett where funeral corteges were a regular sight passing through the town.

Tyne Cot Cemetery is the largest CWGC site and the resting place of more than 11,900 servicemen of the British Empire from Passchendaele and Ypres campaign in the First World War.

Britain also interred the remains of an Unknown Soldier in the nave of Westminster Abbey as a focus of national mourning and to represent all those whose remains were never found or identified. (France did a similar thing at the Arc de Triomphe.) Royal brides in Britain place their bouquets on the tomb in the Abbey - expect Meghan Markle's to be sent from Windsor after her wedding to Prince Harry.