I was provided with an HH5. It's actually quite a decent modem/router, and is comparable in features to your Linksys, If you want to use your own router, then you'll either need to buy a modem/router (to connect directly to the phone line), or buyf a router with a WAN port and persuade the engineer to install a modem and not the HH5. I don't think your existing modem/router has a WAN port, but I could be wrong.
There are plenty of reviews on the HH5 around, and really you need to list what your requirements are. For most domestic purposes the HH5 seems to be satisfactory, but if you have specialist needs than you might need something better, but it's difficult to say.
This is the Trusted Reviews review
http://www.trustedreviews.com/bt-home-hub-5_Peripher...