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Where in Europe can you get broadband speeds as fast as 1 gigabit per second at home, then step outside and surf the 4G mobile web at up to 40Mbps? The answer right now is Jersey.

I've been in the Channel Islands for the last couple of days, getting a quick glimpse of our connected future. Or perhaps a view of a new connectivity bubble, where huge sums are wasted on services for which there is little consumer demand.

In Jersey, the former monopoly landline provider Jersey Telecom is putting fibre-optic cables into a marina development in St Helier. I was shown an apartment hooked up to the fibre, and it certainly seemed to deliver - the 91Èȱ¬ iPlayer streamed effortlessly in HD, and when I tried a few speed tests the needle soared to levels I've never before seen. Downloads did not hit 1Gb/s, but at over 500Mbps, they were more than five times as fast as anything available in a UK home.

It was the upload speed that really impressed - pushing up towards 60, 70 or even 100Mbps. At that kind of speed, live broadcasting from a handheld device would be a breeze. I didn't have time to try that out - but when I popped outside I found another speedy way of getting online or on air.

The technology giant Alcatel-Lucent is working with Jersey Telecom on a trial of 4G, the next generation of mobile phone networks. A mast in St Helier has been equipped to send out a 4G signal promising much faster mobile broadband. One problem - nobody in Europe has a 4G-capable handset yet, so a couple of vans are picking up the signal and sending it out via a wireless network.

I picked up the network on my smartphone, and was soon surfing at speed, even managing a video Skype call in pretty good quality. Again, it was the upload speed that was really impressive - I recorded it at 10Mbps on my phone. While it's hard to see why any home would need a 1 Gb/s connection, there's a clear demand for faster mobile broadband. Smartphones and tablets are now putting ever greater strains on the existing 3G networks, and there's a danger that we''ll hit the buffers before the new networks arrive.

But building either a high-speed fibre network or 4G is an expensive business - and for a market of just 90,000 residents it's difficult to see how that will ever add up. However, Jersey believes that if it projects the island as a high-speed hub, plenty of businesses will want to come and invest. The hope is that data centres will see this as a good offshore location for businesses like online gaming.

Mind you - a near neighbour will have something to say to that. I travelled on to Guernsey, where a local businessman snorted when I told him of Jersey's ambitions: Jersey's a joke, he told me. He was among a couple of people who explained to me that Guernsey was much further down the road of building a cloud industry, with major online gaming businesses already locating there.

There's also no guarantee that places used as test beds for new technology will stay in the lead. A decade ago I made a couple of visits to the Isle of Man, where BT Cellnet was trying out Europe's first 3G network. The company painted an exciting picture of a future where we would all be making video calls and enjoying location-based services. But neither the island nor BT Cellnet - later to become O2 - ended up leading the way in 3G rollout.

So Jersey residents should enjoy their time in the fast lane, because they may not be there for long. But they are doing a useful job, teaching the telecoms industry about the demand for and uses of superfast broadband. And, best of all, they can put one over on their jealous neighbours in Guernsey.