They get airside passes for airside working. I do not know if that would be valid for the discount.
Although it's now a couple of years old the document 'Environment Committee Air Quality and Noise Pollution Around Heathrow Airport. Surface Access Issues informal meeting 3.30pm on 6 December 2011 in Committee Room 2' published by the London Assembly contains some useful data points.
Slide 5 of a presentation
Targets in the current Surface Access Strategy; the target of 40 per cent of air passengers travelling to and from the airport by public transport by 2012 has been achieved, but the higher 45 per cent target had been dependent on Airtrack going ahead. The target to reduce staff travelling to work in single-occupancy vehicles to 65 per cent had resulted in a fall from 71.2 per cent in 2004 to 61.4 per cent. Out of 42,000 parking spaces at Heathrow, 17,500 are for staff. Staff do not pay for parking, but BAA Heathrow, which is required to provide parking for its tenants, can recover the costs as a contribution to its public transport levy, as applies to its public car parks. The public transport levy had provided just over £25 million towards sustainable transport schemes in the last ten years. Theo Panayi described how a decision had been made by the Chairman of BAA in 1994 to invest in public transport. There was no planning requirement to have a travel plan; indeed, at the Terminal 5 Inquiry, the Inspector said that BAA was already doing enough on transport planning.
Slide 7 of a presentation
Incentives and behavioural measures; the introduction of a 75 per cent staff discount on Heathrow Connect had resulted in an increase in usage from 500 staff to 1,700 per month a number that continued to grow. A Heathrow travelcard had been introduced for staff living outside the London area, offering, for example, a £50 monthly ticket from Slough. The travelcard had generated sales of £200,000 and BAA Heathrow was continuing to work with operators to reduce prices and increase passenger numbers. From 2012, BAA Heathrow planned, in conjuntion with TfL, to sell Oyster cards and top-ups to Heathrow staff in the same way as a retailer would, except that the commission is refunded back to the customer. Simon Earles stated that this would give staff high single-digit savings in percentage terms. The scheme is funded through the public transport levy.
Item 9 - Buses
Theo Panayi listed the bus routes that BAA Heathrow subsidises to enable staff to arrive for shifts starting at 4.00am: 350 (Clarendon Road, Hayes to Heathrow Terminal 5), 423 (School Road, Hounslow to T5), 482 (Southall Broadway to T5) and 490 (Pools on the Park, Richmond to T5). This brings the total number of services serving the airport from London and elsewhere to 31 (and soon to be 32), with 13 of them running services that arrive at Heathrow by 4.00am. Theo Panayi indicated that the southern side of the airport had the weakest transport connections, with only routes 482 and 490 serving the southern perimeter.
Heathrow Express and Heathrow Connect
21. Murad Qureshi AM asked what BAA was expecting from Crossrail. Simon Earles stated that the current expectation was for four trains per hour from late 2019, replacing the current Heathrow Connect service. Network Rail has identified an issue of capacity on the Great Western Main Line, with an unmet demand of 5,000 passengers per day from the late 2010s to the mid‑2020s. Network Rail has an option to increase Crossrail services from the planned four per hour to ten per hour, which would remove the Heathrow Express service. Four of these might be services that called at a smaller number of intermediate stations. However, BAA Heathrow estimated that mode share for rail would fall by three per cent if the non-stop Heathrow Express service was withdrawn, because of the number of passengers who use the service for its speed. BAA Heathrow has made representations to the Department for Transport and Office of Rail Regulation for more capacity on the Great Western Main Line.
22. Heathrow Express currently carried 5.5 million passengers per year and Heathrow Connect carries 400,000 passengers. Theo Panayi indicated that many in-bound passengers make decisions about onward travel as they walk out of the baggage hall. Tickets for the Heathrow Express services were now sold in the baggage hall. The added advantage of encouraging passengers to use the service is that once they have tried it they are more likely to become repeat users. Simon Earles commented that at peak times passengers often had to stand on the Heathrow Express.
A general comment - other documents are available on the world wide web which give more information on these and similar topics. One just has to look.