Here, to start you off with yet more inspiration - an excellent profile-view of a T(3):
Click on Image for FULL-RES
Except for one or perhaps two injection-molded (PitRoad?) and/or cast-resin kits - all very rare/expensive, and restricted to 1:700 scale - I have never seen a kit of (any variant of) an RN T-class sub. Ergo, my (first) idea: bash one from the Mirage 400-scale RN U-class sub. Boxed as (at least) Undine, Upholder and the (Polish-transferred) Sokol, this Mirage mold is not only readily available and affordable, but also represents a most "apropriate" conversion - since the U-class hull was apparently itself a scaled-back version of the T-class, as immediately suggested by the following comparison:
Click on Image to Enlarge
Clearly, the diminutive 191-foot long U-class shared key design elements with (at least some of) the considerably larger 276.5-foot LOA T(3) hull - particularly aft, as well as in the core sail structure, and very likely in the upper bow, too. Even better, the largest additions required (green, at bottom) are also among the simplest: a straight tubular insert, flanked by saddle tanks - which latter would be modular additions, in any case. Indeed, the primary difference of the U-class (apart from deletion of the saddle tanks) appears to be a shortened pressure hull - lacking sufficient run to straighten into a cylinder, but instead going directly from tapering at the stern to tapering at the bow.
Again, the match at the bow overall may or may not be quite as indicated - but in any case the lower bow will need some significant expansion. And then some less complex additions to the top casing, from about amidships aft, as well as the gun platforms forward and aft of the sail. The final remaining additions/relocations - tip of the keel, rudder, dive planes, periscope shears, ends of the external torpedo tubes and a couple deck guns - are the simplest, each basically trivial.
Perhaps best of all, however: this conversion builds into a T(3) practically twice as large as 700-scale - and 52% longer than the OOB Mirage Sokol - coming in at 8.98 inches. This corresponds to a scale of 1:370 - about midway between 1:400 and 1:350, and quite compatible with all the older and newer ship kits, respectively, in these two scales.
Of course, for the scale-purist, an exact match with 1:400 could be attained by shaving the beam just a small amount (7.6%, with the crucial points being well hidden under the saddle tanks, anyway), to end up with a T(3) of 8.3" LOA. But if matching to a precise scale, the better (and even nearer) option might be to go just slightly the other way - targeting 350-scale - by (shimming to expand the beam, and length, just 5.6%) enlarging to 9.49" LOA.
Of greatest interest to me about this is its inherent compatibility - which, again as above could even be made to match 100% - with the new, 350-scale Aoshima Ashigara!