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Fro three bikes, a couple of my friends clubbed together and got this
http://www.chainreactioncycles.com/thule-clipon-3-rear-mount-rack-hatch/rp-prod137652
It's super sturdy, but one thing to bear in mind (which I assume is true of most racks) is that you'll have to juggle handlebars - with road bikes / drops we have to take off front wheels so we can rotate the bars/stem to fit.
@gillies that sounds like a good reason - HealTFU and good luck for the ride!
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Does your car have rails to fit roof bars too? If so cross bars are sometimes sold by Lidl and Aldi for under £25 and are good quality.
If not then a roof rack is the first thing to acquire. Search for second-hand on ebay and for cycle carriers to bolt onto them. A lot of people ebay their roof racks as "Vauxhall Astra roof rack" or similar which means you could miss out on one that would also fit your car. So check on Halfords website and search for their own and Thule's racks and see if the ebay "Vauxhall" rack is the same as the "Focus" rack and you could save some cash that way.
branwen
Constable_Savage
Roofbars for two and rear rack for two then you don't have to struggle with getting more than two bikes on the roof. Or get a towbar mounted rack and/or an Erde trailer with bike racks on top. Then get a tent and three dogs and the bitter taste of regret that you're now middle aged.