The B2105 ran from Polegate to Westham in Sussex, following an east-west route between the A22 and the A259. It met the B2104 about halfway along in Stone Cross.
It appears to have been upgraded during the 1935 Road numbering revision to part of the A274 (which the B2105 nearly met in Polegate). In the early 1950s it became part of the A27.
This section of A27 has since been bypassed. The ex-B2105 is now numbered B2247 west of the B2104 at Stone Cross, whilst the eastern section (which was bypassed earlier) is now unclassified.