Unfortunately , I can't give you an exact date. BMW did develop the Tourer along side the Saloon but held back on giving the go ahead for Tourer production. This was possibly as a result of the disappointing sales following the explosive speech by Bernt Pischetsrieder at the 1999 Motor Show, which overshadowed the launch, and must have affected customer confidence in Rover, due to uncertainty as to the company's survival.
Consequently after BMW bailed out and Phoenix took over, the transfer of production facilities from Cowley (Oxford) to Longbridge took place over the summer of 2000 with production restarting in around October that year. The trim tracks and paint shop were commissioned first with the body line and robots coming later due to the additional time in installation. I believe that the earliest saloons built at LB were with Cowley built shells which were stockpiled at LB while the "body in white" plant was installed in LB West Works. At the same time, the plant was adapted as necessary to accomodate the Tourer which were never built at Cowley.
My Tourer was built in Dec '01 and was registered in March '02 and was numbered SARRJxxxxxx245771. I think that the Tourers had serial numbers in the same series as the saloons with a T showing Tourer and L showing Saloon at position 7 in the VIN number. The earliest Tourer I have seen was on a Y plate and had the door engine variant (torpedo) badges which were one of the first Project Drive deletions.
www.austin-rover.co.uk reports that the body in white plant at Longbridge (i.e. producing the primed body shells) was up and running in "early 2001" with the introduction of the estate planned (at the time the article was written) for "mid 2001".
There is however a photograph on the Rover 75 part of this site, ostensibly showing a Tourer on cold weather testing in Switzerland in 1999. It carries the pretty meaningless registration number N269 FYA. The car looks pretty much as the production variant as far as I can tell, but it does have the black sills, as carried by the Cowley built cars. This is likely to indicate, it would have been a hand built development vehicle using as many of the production components as possible. Tourers were afaik all built with body coloured sills at Longbridge. I'm afraid that is the sum of my knowledge.