As investors fret over the health of the British economy, I reckon safe-haven demand for Unilever (LSE: ULVR) could continue to spark in the weeks and months ahead.

Indeed, the household goods manufacturer has edged to record peaks above £37 per share in Monday business, with prime minister Theresa May’s proposed deadline of March 2017 for triggering Article 50, announced at the weekend, creating concern for many investors.

Unilever’s broad worldwide presence has made it one of the few London-listed stocks to endure little-to-no share price turbulence following the EU referendum. The UK represents a very small proportion of total sales, after all, leaving it in great shape to keep on delivering solid sales growth.

The company advised in July that underlying group sales advanced 4.7% during January-June, with the top line driven by ongoing progress in its Asian, African, Latin American and Eastern European marketplaces. In total, like-for-like sales in these developing regions exploded 8% during the first half.

And I believe Unilever’s share price could receive another bump should, as I fully expect, this month’s third quarter trading update (scheduled for Thursday, October 13th) illustrate further solid momentum.

As well as tapping into the rising wealth levels of emerging markets, Unilever is managing to maintain brilliant sales growth through massive marketing campaigns and clever product innovation across market-leading labels like Axe deodorant and Walls ice cream.

So while Unilever may trade on a huge ‘paper’ forward P/E ratio of 24 times — well above the FTSE 100 (INDEXFTSE: UKX) average of 15 times — I believe another solid update will prompt further frenzied buying of its shares, particularly as Brexit-related worries look likely to reign well into the future.

The right medicine

Like Unilever, GlaxoSmithKline (LSE: GSK) could also benefit from concerns over Britain’s economy in the run-up to — and after — the country’s exit from the European Union.

Medicine is one of the last things that falls from shopping lists during times of economic choppiness, making GlaxoSmithKline a solid pick for turbulent times. Besides, the drugs industry is a global phenomenon, immune to the whims of financial difficulties in one or two territories. Indeed, rampant healthcare investment in emerging territories is likely to blast sales at GlaxoSmithKline and its peers higher in the years ahead.

The Brentford firm is due to release trading numbers for quarter three on Wednesday, October 26th. And I reckon this could prove the catalyst for a fresh share price detonation if GlaxoSmithKline announces solid sales growth across its new product lines.

Revenues of these new treatments hit £1.05bn during January-June, leading many to hope that GlaxoSmithKline’s struggles against patent expirations could finally be behind it. And the firm’s pipeline continues to churn out the goods, too — for example, GlaxoSmithKline’s Sirukumab arthritis treatment was submitted for approval in Europe and the US last month, while its Shingrix product also yielded positive Phase III testing results.

GlaxoSmithKline’s transformed R&D operations now makes it one of the hottest long-term growth picks out there, in my opinion, and a forward P/E rating of 17.4 times makes it great value at current prices.

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