The T5 direct service is no more, but Canary Wharf to T2 is very much alive. It's just a matter of changing trains on the same platform. If you look on the EL map on TfL it becomes very clear - the T4 service comes from Kent in via CW, the T5 service is on the Shenfield service which swings through Stratford to the north of CW.

I would not advise doing this anyway, it's far better to go to CW with your bags (or leave them at the Excess Baggage store in T5 or in multiple places in town). It's against the Heathrow By Laws, and what would you do if your next flight got cancelled or re-timed? Your boarding pass would cease to work. Leaving airside is a nuisance anyway, using the transits to T5C and back again. Moreover when you return to T5 then you will not get through security until your boarding pass has been reset for a new Ready to Fly record - visa information API, and so on may need to be reincorporated. You may lose your selected seat along the way too, and you increase the risk of a downgrade.

The set up in LGW is very different, they are not on Ready to Fly.