A FAMILY of four who last week complained that it was hard to get by on a $4,700 a month welfare payment, has actually been receiving extra allowances of $2,000 a month, the Social Welfare Department said yesterday. A spokesman said: ''The family is also entitled to extra allowances to cover payments like water bills, rent, extra diet and telephone charges amounting to about $2,000 each month.'' Wan Choi Yee-kwan was not happy that the $146 billion announced last Friday for government spending in 1994-95 would only mean $10 more a day for her and her three children. The spokesman said Mrs Wan could also apply for other allowances to cover the cost of her children's school reference books. But Mrs Wan maintained only $4,700 was available for disposal each month. ''The additional $2,000 allowances are for regular payments I have to cover and not in my pocket. So only $4,700 is for food, daily necessities and other expenditure. ''It is not enough to cover the high cost of living,'' she said.