There is surprisingly little on the web about it, here are a couple of the more useful posts I've been able to find:
This is what the OED tells us about twitchell and twitten:
twitchel - dial. Forms: 5 twe-, twychel(l, twachylle, 89 twitchel, -ell.
[An alteration, or a variant with different suffix, of ME. twychen, late OE. twichene, OE. twycene, twicen a fork in a road, a forked way.
The form twychen survived in ME. times in Oxford in the names of special passages or lanes: see Wood City of Oxford (O.H.S.) I. viii. 187, 199, 223, etc., and Hurst Oxford Topogr. (O.H.S.) 186, 197. In Lanc. and Yorksh. the reduced form twitch is still in use. Cf. also twitten.]
A narrow passage between walls or hedges.
Twitten - [Perh. related to LG. twiete alley, land; but cf. also OE. twicen and twitchel1.]
A narrow path or passage between two walls or hedges.
Posted by céline on November 16, 2004 8:23 AM
I was born "up the gennel" Bestwood colliery village Nottm. There it refers to the alleyway between the backs of two parallel rows of houses with walled back yards. It was wide enough for the dustbin lorry to drive down and empty the middens that were accessed either side of the gennel via a wooden door set half way up the wall for each house. I understood that a Twitchel was a wide usually hedged alleyway as was a gitty, but more narrow. Whilst an "Entry"was the narrow passage in the middle of a row of terraced houses leading to the backs of the houses, the rooms on the first floor either side covered it over the top making it like a tunnel.
As the latter quote suggests the local terminology may be much more complex. The houses in the picture at the top have 'entries' to the back doors of the middle two properties. This dialect word also survives as a street name, "The Twitchell" in Chilwell, and a Weatherspoons pub in Long Eaton is called the "Twitchel Inn". Nominatim shows other uses, a street in Sutton-in-Ashfield, and a footway in Melbourne, Derbyshire, and, oddly, a street as far away as Baldock in Hertfordshire.