BM -- great looking bike. Are the handlebars & stem from the orginal bike? And have you set it up as a fixie? (hence no brakes?) How much did you spend?
Callm... -- You can check at Crankmeister, as suggested by BM; have seen their posts on FB etc., re: bike (re)builds. Some other shops like RR Cycles Madiwala might also be able to help (with components, if not the build itself); but Crankmeister should probably be the first choice, in BLR. Or some individual folks.
For the new bike you were looking to purchase, if the budget was Rs50K+, and you are able to 'upgrade' your BSA SLR for ~Rs15K, and can use it as a for few years (even as a backup, after you get the new bike), it might be a good spend.
From what I had considered (but never done), a while back -- get the BSA SLR frame checked, to make sure it is good for taking extra stress (which it will have to, after you upgrade it), for many years. Maybe a good simple re-paint (which will also involve removing the old paint, enabling you to check for rust/damage etc.). Then see if you can get used handlebars, brake/gear levers, cranks arms, pedals. See if handlebars+stem & saddle changes, make considerable difference; and then wheels. So keep it as a single speed, initially. Other than the rear hub, I think everything else can be same, if you move to a geared config; then again, you can first go for gears just on the rear, and then decide if you want to have gears on the front as well.
So hopefully you can upgrade in steps, and stop when you feel comfortable enough; and fine tune well, to a specific budget. The BSA SLR cycle frames had a nice look (am thinking of the one i rode long back in my college days), so you can have a good vintage-look-frame, backup bike.
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