You can search nation-wide for Local Quaker Meetings on the national website (Britain Yearly Meeting) here.

The Hampshire and Islands Area Quaker Meeting comprises the following Local Meetings:

Hampshire:    Alton   Andover  Basingstoke   Hythe   Portsmouth
                     Southampton   Winchester
Isle of Wight:  Isle of Wight
Channel Islands:   Alderney   Guernsey   Jersey

(Maps not to scale: the Isle of Wight is twice the area of the combined Channel Islands)

Other meetings in Hampshire and neighbouring counties are here.

 

Other Local Quaker Meetings in the County of Hampshire are:

   Lymington and New Milton (contact both via Bournemouth Coastal Area below)  
   Farnborough (contact via Surrey-Hampshire Border Area below)

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Local and Area Meetings (with website details) in neighbouring Counties include:

   Bournemouth Coastal Area (Bournemouth, Lymington, New Milton, Poole, Swanage)
   Dorset and South Wilts Area (Bridport, Dorchester, Lyme, Salisbury, Shaftesbury, Weymouth)
   Surrey-Hampshire Border Area (Note - this is a test site: Farnborough, Farnham, Godalming, Guildford, Woking)
   Surrey and Sussex Quakers (Capel, Coolham, Dorking, Horsham, Ifield, Leatherhead, Lingfield, Oxted, Reigate)
   Mid-Thames Area (East Garston, Henley, Maidenhead, Newbury, Reading, Wallingford, Wokingham)
   Chilterns Area (Amersham, Aylesbury, Chesham, Chorleywood, High Wycombe, Jordans, Slough & Windsor)

   Also some details for Sussex West on the Worthing website here (Bognor, Brighton, Chichester, Ditchling,
    Littlehampton, Midhurst, Shoreham, and Worthing)