Upvote:1
On your outbound journey - as you hold a valid US visa, you may not need a transit visa, if you can meet the exemption criteria:
Exemptions You won’t need a visa if you:
- are travelling to Canada, New Zealand or the USA and have a valid visa for that country
- are travelling from Canada, New Zealand or the USA and it’s less than 6 months since you last entered that country with a valid entry visa
- are travelling to or from Australia and you have an Australian visa sticker in your passport - Australian e-visas and paper confirmation slips aren’t accepted by UK border control
- have a valid US permanent residence card issued on or after 21 April 1998 (or an I-797 extension letter issued by the Bureau of Citizenship if it’s expired)
- have a valid Canadian permanent resident card issued on or after 28 June 2002
- have a valid uniform format category D visa for entry to a state in the European Economic Area (EEA)
- have a valid uniform format residence permit issued by an EEA state
Otherwise you'll need to apply for a DATV.
On your in-bound leg, you will definitely need a visitor visa as your stay period is longer than the 48 hour that is provided for visitor in transit visas.
For the application process apply online and then visit your nearest VFS office. It takes 3 weeks (at most) for the visit visa.
but the eligibility criteria for that visa says that you are "not in transit to another country, except for Ireland, the Isle of Man or the Channel Islands".
What this means is that if you are transiting, this is not the visa for you - you'll need either the direct airside transit visa or the visitor in transit visa. However, the maximum you are allowed to stay is 48 hours which disqualifies you for those.