import requests # pip install requests

postcode = 'SW1A1AA' # Or whatever postcode you're looking for
uri = "https://mapit.mysociety.org/postcode/{0}".format(postcode)

response = requests.get(uri)
response.raise_for_status()

json = response.json()

constituency_code = str(json['shortcuts']['WMC'])
# u'65759'
constituency = json['areas'][constituency_code]
# {u'codes': {u'gss': u'E14000639', u'unit_id': u'25040'}, u'name': u'Cities of London and Westminster', u'country': u'E', u'type_name': u'UK Parliament constituency', u'parent_area': None, u'generation_high': 30, u'all_names': {}, u'generation_low': 13, u'country_name': u'England', u'type': u'WMC', u'id': 65759}