Decent railway companies like South West Trains let you upgrade to 1st Class for just £5 per person each way for any length of journey on their network. Provided there is room, all you have to do is find your seats in 1st Class and then present your Standard Class ticket to the guard and ask for the £5 upgrade before he asks to see your ticket
Ahhhh - can't find any mention of it on East Coast lines.
Our local operator allows onboard upgrade for £7 at weekends and normal excess fee during the week. Try phoning again when the shifts have changed to see if you get a different more helpful person.