To get more real speed from a 400-speed emulsion measured as shadow detail with relatively normal contrast, it's best to use a developer like Acufine, Diafine, or Microphen. Other developers will increase contrast with extended development times, but won't improve shadow density, and all you will have will be contrastier underexposed negatives--sometimes not a bad thing, but maybe not what you are after.
My preference is Tri-X 400 at EI 800 in Acufine, but if you want to stick with Ilford products, HP5+ may not be a bad choice and you could try their recommendation in Microphen.
Alternately, Delta 3200 is really an ISO 800 film, so you might try that. There are some good recommendations for it at: