Circular Search view not returning results if city exists in UK AND elsewhere
The Geofield proximity Views filter doesn't have any default location settings. The filter passes the given string value on through to the geocoder without any additional settings:

  $geocoded_data_raw = geocoder($geocoder_engine, $location);


As such, your only option is to form alter the submitted data as answered in this question:

/**
 * Implements hook_form_views_exposed_form_alter().
 */
function MYMODULE_form_views_exposed_form_alter(&amp;$form, &amp;$form_state, $form_id) {
  array_unshift($form['#submit'], 'MYMODULE_form_views_exposed_form_submit');
}

/**
 * Modify submission value with " UK" if given origin has been supplied.
 */
function MYMODULE_form_views_exposed_form_submit($form, &amp;$form_state) {
  if (isset($form_state['values']['field_geofield_distance']['origin']) &amp;&amp; 
      strlen($form_state['values']['field_geofield_distance']['origin']) &gt; 0) {
    $form_state['values']['field_geofield_distance']['origin'] .= ' UK';
  }
}