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You would need to connect via either a BT openreach modem or other VDSL modem such as the Draytek130. The HH6 does not have a modem only mode.
The DrayTek Vigour 130 can be had for under £80. If you see someone selling it for £200+ then they are trying to work a con. The Openreach modems haven't been issued for around 3 years and can only be obtained second hand and naturally will have no warranty. All should work fine with an OR modem.
You could have a look at the TP-Link VR600, plenty of features. If you want all the bells and whistles the Synology has then the cost for other makes will be about the same.
I assumed you had already bought a Synology router and just wanted to make sure it would work with an Openreach modem. There are plenty of combined VDSL modem/routers on the market and most (if not all) have those sort of facilities these days, just have a look at the manufacturers specs to decide which features you require.