There are a few BAFRA restorers in Kent, any one of them will be able to do a sympathetic restoration for you. As cabinetman stated, if someone has sawn off the rack they would have sawn through the back legs which would not make the repair straight forward but in the right hands could still be successful. If it is just the bars missing then it would be an easy repair, if period oak was used with an old surface being retained for the forward face it would be hard to tell it was a replacement.
The photo below shows the construction from the back of a sideboard. If you have a sideboard with a panelled backboard it would make the repair more expensive but still achivable.