The odds of a Brexit appear to be falling. As I write, opinion polls suggest that the UK is leaning towards voting to stay in the EU.

But there’s still some uncertainty priced-into the market. A convincing Remain vote could trigger a strong rally but one consequence of this would be that many of the high dividend yields on offer at the moment could fall sharply.

I’d expect this effect to apply most strongly in the housing and financial sectors, both of which could also be hit hard by a Leave vote.

7% in 2017?

Investors in Lloyds Banking Group (LSE: LLOY) may be disappointed with the performance of their shares, but the bank’s dividend progress has been much more satisfactory. Last year’s total payout of 2.75p beat City forecasts.

Lloyds is now expected to pay out 4.24p per share in 2016, giving a 6% yield at a share price of 70p. In 2017, the bank’s payout is expected to rise again, giving the shares a 7.1% prospective yield.

If Lloyds continues to deliver on current forecasts and the UK housing market remains in good health, I think its shares are likely to rise. Buying now — while the market is uncertain — could be the last opportunity for a long time to lock in such high dividend yields.

Of course, as Foolish investors we need to consider what could go wrong with this plan. The most obvious risk is that the housing market will slow down, putting profits from mortgage lending under pressure and threatening a rise in defaults. As the UK’s largest mortgage lender, Lloyds is very heavily exposed to the housing market.

However, I think Lloyds may be worth the risk. The bank’s shares trade on a forecast P/E of 9.3 and at just 1.3 times their tangible net asset value. That seems reasonable to me.

Better to invest directly in housing?

Another company that could be hit hard by a downturn in the housing market is housebuilder Barratt Developments (LSE: BDEV).

Barratt shares are down by about 10% so far this year, but the group’s latest trading statement in May was very positive. The firm had forward sales of £2,844m in May, 9.7% higher than at the same point last year.

In recent updates, other housebuilders have also confirmed that trading has been unaffected by the EU referendum. It appears that for UK house buyers and mortgage lenders, business is still good.

Barratt’s balance sheet is also very attractive. The group expects to have net cash of £300m-£350m at the end of June and in February confirmed plans to return a total of 67.8p per share to shareholders by November 2017.

That equates to a yield of about 12% in less than two years. Payments for the current year are expected to total around 30p, giving a forecast yield of 5.4%. This payout is then expected to rise by around 25% in 2017, giving Barratt a 2017 forecast yield of about 6.7%.

Barratt shares currently trade at around twice their tangible book value and on a forecast P/E of 10. I believe this is cheap enough to make further gains likely, especially if the UK votes to stay in the EU.

Today's top dividend buys?

If you already own shares in Lloyds and Barratt and are hunting for more top dividend buys, I'd urge you to consider 5 Shares To Retire On.

The Fool's dividend experts have hunted through the FTSE 100 and selected just five stocks they believe have the potential to be long-term winners.

Together, we believe an investment in these five companies could make a significant difference to your long-term wealth.

This exclusive report is free and carries no obligation.

To receive your copy today, simply click here now.

Roland Head has no position in any shares mentioned. The Motley Fool UK has no position in any of the shares mentioned. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.