Did you follow the manual to do wifi clone? You may follow the instruction to do the clone, then the tp-link will have the same wifi name as your main router.
http://uk.tp-link.com/faq-398.html

Actually there is no way to make sure the wifi won't disconnect even if you have done the wifi clone, however the disconnecting time will be short according to the performance of different clients.

Thanks flying snow. I did try this previously, but I think I may have made a mistake

Will try this again later and report back.

You need to set all the WiFi access points to the same SSID and passphrase, including the 2.4 and 5 GHz choices. Even then, it is entirely up to the client device how, when and how often it looks for a stronger connection. Many smartphones tend to cling to what they have, no matter how weak, and only scan for a new connection when they lose the existing one completely.

There is a new method, "mesh WLAN", available in the very latest products from prime manufacturers. This makes the WLAN APs aware of each other, and allows letting the WLAN AP mesh do the connection steering.

This is of course not implemented in the hardware you have - and it essentially requires all the WLAN APs to be from the same vendor and on the same firmware level.