Buying train tickets in England

yes - just buy on the day - no savings to be made buying beforehand

http://www.nationalrail.co.uk/times_fares/ticket_types/46548.aspx

You can get an Off-Peak ticket right up to departure time, yes. However, if you are able to pin yourself down to a specific train time in advance, you can buy discount advance tickets weeks or a couple of months in advance that are significantly cheaper than off-peak for most long-distance routes.

the OP asked about Off peak tickets, and only Off peak tickets, so his/her understanding is correct

Advance tickets are an entirely different ticket category

The OP doesn't ask about Advance tickets. The OP asks about off-peak tickets. There is no cost advantage in buying these before the last minute, but you might want a seat reservation on a busy service, which is possible even in off-peak times.

I don't think 'Advance' is a good name really since nearly all tickets can be bought in 'advance'; then again coming up with an alternative one word descriptor isn't easy.

The types of ticket are for the full picture:

Advance - Buy in advance, sold in limited numbers and subject to availability. These tickets are only valid on the date/train specified.
Off-Peak - Buy any time, travel off-peak.
Anytime - Buy any time, travel any time.
Season - Unlimited travel between two stations for a specified period.
Rovers and Rangers - Unlimited travel within a specified area. There may be a few time restrictions on when you can travel.

And then there are two general divisions within Anytime and Off-Peak tickets, which are Day and period.

Day returns need to be completed before the end of the travel day, usually either 3am or 4.30am the following day; period returns usually are valid for up to 28 days on the return trip.

Not all ticket types are available on all routes and flows.

Here is a site that gives advice about buying train tickets. To be honest, the system is bonkers yet nobody seems willing to sort it out.
http://www.moneysavingexpert.com/travel/cheap-train-tickets

It has defied 'sorting out' since removing some of the historical layers of complexity and discounting and regional pricing would result in some fares increasing significantly, off-peak day returns being the most obvious category.

Yes, as Marco says, it is sometimes better to leave Pandora's box firmly shut.

Many of those deals that can be sniffed out are due to pre-privatisation history, and who sets the pricing for each flow, and various government interferences over the years.

If it were to be all rationalised split ticket savings would evaporate and the overall prices would likely rise significantly.

It is already considerably simpler than it was a few years ago, although we still have a few holdovers in names such as many people knowing Super Off Peak Period Returns as Super Savers (Super Off Peak likely would disappear under some rationalisation plans).

renelmiller (OP),

is this making any sense to you?

and about those Off-Peak Day Returns, mentioned by Marco. On many flows the single (one way) is only 10 pence less than the Off Peak Day Return. If rationalised, I can't see the 10 pence return lasting long....

Thank you everyone for your responses. Yes, Nigel, it is making sense. It has been over 30 years since we have travelled by train in the UK and, at that time, we just bought the tickets when we were ready to travel. I have looked up the trips we are interested in and the prices for the Off-peak trains seem to be much less than the other trains. Our trip is in just over 5 weeks, so we may have already missed the best prices for advance purchase tickets. If the Off-peak prices won't go up, it would give us more flexibility to purchase them when we are ready to go.