On a T5-T1 connection, you're very unlikely to be able to enter T3 on your own. In theory you shouldn't be able to, but there have been reports on FlyTalk of the odd person managing it (though normally by mistake!)

Heathrow offers a Reserve And Collect service, so if you know what you want you can order online

If you had a longer transfer, you could book the Terminal Shopping Transfer service, but that requires a >3 hour layover and a promise to spend >£250. Sadly your transfer is too short for that, so I think the Reserve And Collection service is likely to be your best bet