The A2050 follows the route of the old A2, heading into Canterbury from Harbledown, and exiting towards Bridge. The western half of the road is labelled in at least one place as the A2039 but this is likely to be a mistake.
Harbledown – Bridge
Looking northwest along the New Dover Road towards Canterbury
The road leaves the A2 at a limit access junction near Harbledown, where it is signed as (A28). The road becomes two-way and the limit drops for 50mph, presumably due to a few closely spaced junctions. The road heads round to the southeast and passes under a footbridge before becoming dual carriageway, with the limit dropping to 40mph. At the first roundabout, the road carries straight on, with an exit to the left leading to the A290. The road continues as D2 down to St. Peter's Roundabout where it TOTSOs to the right. It may have a useless multiplex here with the A290, but there is not sufficient signage to know. The road curves around to meet the A28 at Wincheap, where it begins a short multiplex around the south of the city walls. At the end of the High Street, the road leaves its multiplex and TOTSOs to the right, where it is signed as (A257). The road is D2 and passes alongside some shops. After a set of crossroads, where the A257 turns off to the left, the road becomes two-way again and starts to become more residential and less commercial.
Frontages start to thin out and then it is a clear blast out to a roundabout for the New Dover Road P&R (which, like all the P&R facilities in Canterbury, is excellent). The road is now rural and NSL and leads straight down onto the A2 at a back to front junction at Bridge. There's a one-way link from that village to the A2050 but getting to it requires a detour via the A2.
Brenley Corner writes:
An excellent description. It may be worth adding that it follows exactly the route that the A2 took through Canterbury before the A2 bypass was opened in 1980.
It is also interesting to note that the A2050 number is only admitted in two places: Canterbury-bound through Harbledown on the ADS for the first crossroads, and a roundabout exit sign Canterbury-bound on the Dover Road park & Ride site roundabout. So far as I know the A2 exit signs at either end onto the A2050 sign it as "(A28)".
This is probably only an A road for administrative purposes rather than any routing significance - most of it multiplexing, as Martin says, with the A290 and the A28
It may have a useless multiplex here with the A290, but there is not sufficient signage to know.
According to my maps, the part of Rhiems Way connecting St Peter's to the Wincheap roundabout is in fact part of the A290, although it is not signed as anything.
At the end of the High Street, the road leaves its multiplex and TOTSOs to the south, where it is signed as (A257).
I wouldn't say it TOTSOs here. The A28 and A2050 never actually meet either. St George's Street is part of the A257, which then TOTSOs at the crossroads, turning left. The A2050 then resumes straight on. St George's Street is signed "Sandwich A257" (no brackets) and is marked as such in my atlases.