単一のクエリで複数のグループを使用する

最初のカウントをサブクエリに入れる必要があります：

SELECT  COUNT(CASE WHEN C = 1 THEN 1 END) AS nooffamiliesHavingcount1,
        COUNT(CASE WHEN C = 2 THEN 1 END) AS nooffamiliesHavingcount2
FROM    (   SELECT  COUNT(*) AS C
            FROM    TableName
            GROUP BY House_No
        ) t
WHERE   c IN (1, 2);

編集

カウントで範囲を設定する必要がある場合は、次を使用できます：

SELECT  COUNT(CASE WHEN C <= 1 THEN 1 END) AS nooffamiliesHavingcount1,
        COUNT(CASE WHEN C BETWEEN 2 AND 4 THEN 1 END) AS nooffamiliesHavingcount2,
        COUNT(CASE WHEN C > 4 THEN 1 END) AS nooffamiliesHavingcount3
FROM    (   SELECT  COUNT(*) AS C
            FROM    TableName
            GROUP BY House_No
        ) t

SQLフィドルの例