This price of 2 x £18 = £36 for two First Class Advance Leeds - St Pancras singles can be reduced to 2 x £17 = £34 by booking through the
East Midlands Trains site. From the front page, click on
Click here for more options. After entering Leeds to London St Pancras, choose "Go via Barnsley". This ensures a local Northern service from Leeds, and avoids the faster CrossCountry services, which are very unlikely to have Advance fares available for this journey at short notice. As
sonic2009 says, there is no First Class accommodation on the Leeds - Sheffield leg by this route.
Two Advance First Class singles can currently be bought for a total of £34 on the 1037, 1105, 1205, 1805 or 1905 departures on 11 August.By entering "via Barnsley", you have opened up First Class Advance tickets for this leg too. I am finding a fault at present where, despite the "via Barnsley" instruction, for the return leg the booking engine is suggesting a walk from St Pancras to Kings Cross followed by an East Coast train to Leeds avoiding Barnsley.
To overcome this if necessary, search for each leg separately as single tickets. There are none left northbound for £17 on 13 August, but you can get two First Class tickets for £27 each, a total of £54, for the 0637 from St Pancras, or 2 x £33 = £66 at 0955, 1055, 1155 or 1255.