From London or Sussex, take the M25, M4 to junction 15, then A419 near Swindon. This dual carriageway bypasses Cirencester and becomes A417. Turn north on the M5 (signed the Midlands). At junction 8 join M50, and leave at junction 2, on A417 past Ledbury (follow 'all routes', then A438 signed Hereford but DO NOT GO INTO HEREFORD - it can be very congested). Soon turn off at Trumpet Inn/ traffic lights onto A417 signed Leominster. Turn right at end, on A49, then first left at roundabout on B4361 to Leominster (Newton Farm cider, on left almost immediately, sells excellent cider from the barrel). In Leominster, turn left at mini roundabout, and turn left at traffic lights on A44, signed Rhayader. After 14 miles this bypasses Kington. (An ALTERNATIVE route is up M40 towards Birmingham, then M42 west/M5 south to junction 7, then A44 west - very quick if Birmingham area not too busy.)
The cottage is at the west end of Weythel.
There is a surprisingly good bus service (Sergeants Buses; bus 461/462/463); not Sundays or Bank Holidays but runs Good Friday) from Hereford to Llandrindod Wells, leaving from Hereford station and going via Kington (where you may have to get off the bus and then board the same bus a few minutes later): ask to be dropped off at Stanner, by the Welsh border, from where it is a 2.5 mile/4km walk along the road.
It would be feasible to cycle from Hereford or Leominster if you do not have too much luggage. Leominster is the nicer option. From there it's about 19 miles (fairly level): to get to Leominster from London Paddington, travel to Newport and then change (journey time about 3hrs 30mins). Alternatively you can take bikes on the Oxford to Hereford line, where you can cycle from Hereford (27 miles) or Ledbury (40 miles), or change at Hereford for Leominster.