Teddington beat Hounslow, winners for the last three years, 4-2 on penalty strokes after drawing 2-2, and will be playing in their third successive final. Two goals in seven minutes just before half-time were fair reward for Teddington's early superiority.
Jason Laslett opened the scoring in the 26th minute before Philip McGuire converted a penalty stroke.
Robert Thompson put Hounslow back in contention with a penalty-corner goal early in the second half and scored the equaliser 11 minutes later.
It took a good double save by Meredith to deny Thompson yet another corner, and Meredith produced another useful save to thwart Nick Gordon in extra time.
In the other semi-final, Old Loughtonians, who beat Reading 3-2, looked the more likely winners from the third minute, when Nick Thompson gave them the lead from the penalty spot.
Paddy Osborn equalised with a penalty stroke before Barker scored from a penalty corner, as did Osborn at the other end to make it 2-2 at the interval.
The winner came in the 53rd minute, Paul Krishman sweeping in a rebound from Thompson's penalty-corner shot.
Colin Banton's only league goal of the season saw Slough beat East Grinstead 1-0 in the final Pizza Express game of the season and retain their First Division place. St Albans are relegated along with Bromley.