We will travel by train from Paris to London early Jun. Is the Eurostar the best way to travel on a budget?> Should i buy tickets ahead for familyof 5 to get the best price?

Yes buy your tickets ahead. You can book up to 90 days out . You might find it cheaper to buy a round trip and toss the unused portion away.

Eurostar pricing is like airfares- different prices for more or less popular trains/times - definitely buy in advance to get best fare (walk up fares can be 3 times as much) - so buy tickets as soon as your travel date/time is final. Also realize this is not like taking an ordinary train - you can;t just walk up and get on - there is check in and security -so you need to arrive in advance - like for a plane trip.

We bought Eurostar tickets from London to Paris 2 weeks ago for our trip in June. The fare depended on the time of day traveling, class of seat and if the ticket was non-refundable. We purchased one way, non-flexible, a.m. tickets for 4(2 adults, 2 teens) for 260(GBP). We were able to choose our seats and there was plenty availability. I don't know if this was the absolute least expensive way to go but it felt reasonable and it was easy to book on line.

The budget option is Eurolines coach. But only if budget is the overriding concern

You can book up to 120 days in advance on the official site, www.eurostar.com. Book NOW! If you wait, the price will only increase. If you buy your tickets at the last minute, they will be very expensive.

The "trick" of booking return (roundtrip) tickets and throwing away the unused portion used to be a good idea because return tickets were cheaper than single (one-way) tickets. That's no longer true. You'll be better off booking single tickets.