Try this:
$sqlquery = "UPDATE $table SET name='$name', street='$street', city='$city', county='$county', postcode='$postcode', phone='$phone', fax='$fax', email='$email', website='$website', c_council='$c_council', d_council='$d_council', stat_dev='$stat_dev', trad_act='$trad_act', org_type='$org_type', enq_sourc='$enq_sourc', init_contact_date='$init_contact_date', legal_struct='$legal_struct', keywords='$keywords', null_field='$null_field', descr='$descr', gender='$gender' WHERE client_id='$client_id' ";
Removed quotes from around table name, added commas, moved where clause to end of sql.