Correct, one does need a switchbox. Try Keene Electronics, they have a number of differing devices that might do for you . . .

Code
BT22 @ £9.99 - Simple two way manual.
SSB @ 19.99 - Three way manual.
BT921 @ 39.99 - Four way (3 scart, 1 composite) manual.
BT945 @ £69.00 - 5 way auto (with remote)
SBX99SE @ £69.99 - 5 way auto (with remote). Very similar to the BT945.
HRS1000 @ £95.00 - 6 way matrix switch with remote. (6 inputs to any one of 3 outputs).
KSC @ £149.99/£249.99 - Keene's own Scart Commander. 4 to 1 or 7 to 1, if using the master/slave configuation.

PS
I use a BT941, the forerunner of the BT945, and find it very good.