How do I query taxonomy OR custom field in Wordpress at the same time?

Question

I need to query wordpress posts returning results that could be matched either by the category OR custom field. Using the below code only returns results if they are matched by the category AND custom field. I need to find matches where it could be matched by either query, so an "OR" result but doesn't seem to work.

Can anyone help?

$args =  array(
'post_type' => 'post',
'tax_query' => array(
'relation' => 'OR',
    array(
        'taxonomy'  => 'category',
        'field'     => 'slug',
        'terms' => array( 'arts','food' ),
        'operator'  => 'IN'
    )
),
'meta_query' => array(
   'relation' => 'OR',
    array(
        'key' => 'birth_city',
        'value' => 'London',
        'compare' => 'IN',
      ),
   )
);

Answer 1

Version 0.2

Here's a simplification of my previous answer - I hope you don't mind me adding it as a new answer, to avoid confusion with my previous one.

Here I use the WordPress functions get_meta_sql() and get_tax_sql(), to modify the WHERE part of the SQL generated by WP_Query():

 /**
 * Class WPSE_OR_Query 
 * 
 * Add a support for (tax_query OR meta_query) 
 *
 * @version 0.2
 * @link http://stackoverflow.com/a/22633399/2078474
 *
 */
class WPSE_OR_Query extends WP_Query 
{       
    protected $meta_or_tax  = FALSE;
    protected $tax_args     = NULL;
    protected $meta_args    = NULL;

    public function __construct( $args = array() )
    {
        add_action( 'pre_get_posts', array( $this, 'pre_get_posts' ), 999 );
        add_filter( 'posts_where',   array( $this, 'posts_where' ),   999 );
        parent::__construct( $args );
    }
    public function pre_get_posts( $qry )
    {       
        remove_action( current_filter(), array( $this, __FUNCTION__ ) );            
        // Get query vars
        $this->meta_or_tax = ( isset( $qry->query_vars['meta_or_tax'] ) ) ? $qry->query_vars['meta_or_tax'] : FALSE;
        if( $this->meta_or_tax )
        { 
            $this->tax_args  = ( isset( $qry->query_vars['tax_query'] ) )  ? $qry->query_vars['tax_query']  : NULL;
            $this->meta_args = ( isset( $qry->query_vars['meta_query'] ) ) ? $qry->query_vars['meta_query'] : NULL;
        }
    }
    public function posts_where( $where )
    {       
        global $wpdb;       
        $field = 'ID';
        remove_filter( current_filter(), array( $this, __FUNCTION__ ) );    

        // Construct the "tax OR meta" query
        if( $this->meta_or_tax && is_array( $this->tax_args ) &&  is_array( $this->meta_args )  )
        {
            // Tax query
            $sql_tax = get_tax_sql( $this->tax_args, $wpdb->posts, $field );            

            // Meta query
            $sql_meta = get_meta_sql( $this->meta_args, 'post', $wpdb->posts, $field );

            // Modify the 'where' part          
            if( isset( $sql_meta['where'] ) && isset( $sql_tax['where'] ) )
            {
                $where  = str_replace( array( $sql_meta['where'], $sql_tax['where'] ) , '', $where );
                $where .= sprintf( ' AND ( %s OR  %s ) ', substr( trim( $sql_meta['where'] ), 4 ), substr( trim( $sql_tax['where'] ), 4 ) );              
            }
        }   
        return $where;
    }
}