I used to use an early +8 silencer on my TR +4 back in the day. This gave a a nice deep melodious sound on idle , rising to a nice scream at 4,000 rpm.
Thsi was the large oval shaped unit. It bolted up directly on the bottom of the Y piece of the manifold, and like you I used a side exit exhaust at the back
Nowadays there are probably better alternatives available from any number of sources. As you are near Bristol I would start with a call to Williams near Chipping Sodbury.