Let's do some sums:
Say the average car gets 50mpg (overestimating by a lot).
That's 11 miles per litre, or up near me that's about £1.17 / 11 miles (11 pence'ish per mile)
From
wikipedia a litre of petrol contains 34.5 mega joules of energy.
That means that you need around 3 mega joules of energy per mile in a pretty efficient car. (note this will assume the combustion efficiencies of petrol and hydrogen will be the same, which is probably not reasonable (H2 will be more efficient than petrol)).
Price of electricity is apparently 13p / kWh (from
here, which means for 13p you get 3.6MJ. (the price was the most up to date I could find, but seems a little high to me, maybe someone else can find a better value)
Since you need 3 MJ per mile, it costs you 13*(3/3.6)=10.8 pence, or 11 pence.
I.e. You won't save any money, it will cost about the same. And the above is assuming that the electricity->fuel conversion is 100% efficient, which it won't be even close to. There's a reason the two numbers come out the same. The price of oil and other power is linked (whether genuinely or artificially), for a home user, there's no getting away from it.
As for the video that was on ebay, it says you get up to 2 litres per minute of gas being produced, which is about 0.0015 moles of gas per second (H2 + 1/2 O2). The heat of formation of water is -285kJ/mol, so they needed to be putting in 428W of electricity to generate that amount of gas.
Combining the stuff above, we see that you need around 10 litres of gas to generate the required 3MJ / mile. That would take five minutes. There's no storage medium that I can see, so the gas must be generated 'in situ'. That means you're running off the battery. From a quick google, a car battery will produce 10kW for a short period. Let's be very generous and say that's 5 minutes. That gives you 3MJ of energy contained in the battery, or enough for 1 mile. After that, you're burning up petrol to convert into electricity to convert into hydrogen to power the car.
As you may have guessed, I think this is a load of BOL***KS. It's nothing more than a well known electrolysis cell (which by the way will need fairly strong acid to work properly, and is even shown in the video!). Not to mention the danger of having litres of gaseous hydrogen in a car. It'd be lethal. Please don't buy one of these. Common sense should tell you it won't work. If it did, it sure as hell wouldn't be up on ebay for £150.