The 737NG has IRS, GPS, DME, VOR (two of each) all of which feed into to FMC which computes the best composite position to navigate with. However the standard arrival routes are still based on the VORs.
The standard arrival route is the LOREL 2Q: GURLU - MAY - VATON (near Heathrow) - BPK - BKY. As given this route goes round the western side of London, but sometimes ATC offer a short cut before reaching VATON direct to BPK, or sometimes a radar vector folowed by direct to BPK or BKY. This could take you nearer the center of London.
UK and Irish airlines do not permit flight deck visits.